Problem 55985. Generate Tribonacci Sequence

Created by Ben Placek

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{"parts":[{"partUri":"/matlab/document.xml","contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?><w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>The \"Tribonacci\" sequence is an extension of the idea of the Fibonacci sequence:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"true\"/></w:customXmlPr><w:r><w:t>T_{n+1} = T_n + T_{n-1} + T_{n-2}</w:t></w:r></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>That is, each new term is the sum of the three previous terms.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>If the sequence starts with 0, 1, 1, the first 10 Tribonacci numbers are: 0, 1, 1, 2, 4, 7, 13, 24, 44, 81.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>If the sequence instead starts with 2, 3, 7, the first 15 Tribonacci numbers are: 2, 3, 7, 12, 22, 41, 75, 138, 254, 467, 859, 1580, 2906, 5345, 9831.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Given a vector of three numbers, </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>Tstart</w:t></w:r><w:r><w:t>, and an integer </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>n</w:t></w:r><w:r><w:t> (&gt; 3), return an </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>n</w:t></w:r><w:r><w:t>-element vector of the first n Tribonacci numbers starting with </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>Tstart</w:t></w:r><w:r><w:t>.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[T = tribo([2 3 7],15)\n    T = \n    2 3 7 12 22 41 75 138 254 467 859 1580 2906 5345 9831]]></w:t></w:r></w:p></w:body></w:document>","relationship":null}],"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","target":"/matlab/document.xml","relationshipId":"rId1"}]}

<div style = "text-align: start; line-height: 20px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: normal; text-decoration: none; white-space: normal; "><div style="block-size: 283px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; vertical-align: baseline; "><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="">The "Tribonacci" sequence is an extension of the idea of the Fibonacci sequence:</span></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="vertical-align:-6px"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAScAAAAoCAYAAAC8ezwgAAAAAXNSR0IArs4c6QAAAERlWElmTU0AKgAAAAgAAYdpAAQAAAABAAAAGgAAAAAAA6ABAAMAAAABAAEAAKACAAQAAAABAAABJ6ADAAQAAAABAAAAKAAAAABTNuOYAAAIt0lEQVR4Ae1cWYwVRRRlG0EFQRARRRwDiHHXKKgohl0jYyIJ0SAJRlnUEPVD/8QIH36oibiAikSNYTGCSFSIODIgCEhEDBoIBiNRFBQhLgQFEfScma559fp19+ulul8v9ybnVdWtW9vp29VV1T3Tpo2IMCAMCAPCgDAgDAgDwoAwIAwIA8KAMCAMCAPCgDAgDAgDwoAwIAwIA8KAMCAMCAPCgDAgDAgDrQy0bY2VR4Yh+W65KlDqGKwHAL8HKlU841UY8uAIw34RZR+LUD7pouJX8TGeO1/q4MLVGOi7Wnn7ETYBe4HDwAxAyUZElgP1AMv0Ayi7AZmYmqlw/emCnOEAr8Fx4HPgC+AQcCMwBFAyExHa3AAw72SAsqslyMyv+FU8l6pQvrQVHHL1MwVoq/F5NuL/aZio5TE61cqbZ9NLspKB2yyuNiPsbcsmf4rnb215pyG908rn9ciSiF/Fc7UK40s9wd8J4H4HHidBp24a2pxps6lDmpPaeJtekpUMvADVd8AplVnNK0/F8xyHfK6ktjvoTau4tV8HjDNQsfhViUROJuT1/ZIqUiwLvhRpgKowJ5YdQHul0MIFiKubhlsQJzkKZQ+nDNGVMcDJZUKZpiXRH4HimGGDgw3PmZ5z0JtW7UOF7MN0AxWLX5VInGbxeqCkihTLgi9FGqAqzCd5L5XQQm7vfgHUjfOklqeitOG5gkh1Bs6HCfmyywNQKI450Xe2GyA9EKh30JtWmZycxK9KV8f05JQFXyqNPobY5ahT3TQMh8bQhlTZ8pZU8dxUY0JMTk5uQymiX5menNy45bY8Lb7k1kdXfTvXnMqM0ZrqEOKbtLREzTDAN3d8g6eEr4fzLuJX8VzhzPsSB+BXRmmGqxHnwXcehN8ZrTQwEJ7B6TdamCoHoRDfxin5UEVyHObVr2p9yTLvS34np05gmt/XKMnTTUMOuquBRQj1SSVsNfrkxi3VtrAVZaRcnv2q1pcg877kd3LixERHUpKn7QbfdPAMIKr8ELUClNdXER8ZqC/tVeTZr2rNfWF86SkwrQ7W+AGgiHkGuqJKbpUVz3eab6KixmXQHPQAv2Vjfw572LA8v1wPI3n1Kx4VePFKPskr+fWyC/sdVC18CUMxK35XTvoSMY2rpjrQcg/A1V0S3/+YvQottQ1DoK4HnbYxjkZsdXZB2s+Wlp8BEG5C/sNIXv3K71EBPyXx4j/sUUEtfMnv9b8AhlOAi4G9wFpgIcDJukzUzVCmtCX4zdNlmi5N503s/ySAHyXWA68AWZVRWse3IM4natzyBBpY4tGI4nMpbLwmy2886nDLyrNffYlB8wZ0exvegLyxwFHgQcBNeO4YRmrhS376OQZG/LxB/W0oy9wL8A31ZIAP5UByF6w5qxFHAK8nKLIjCz86vASo81HTlbC5A3gJYP9eBoLKYBTwWlr7zYt6RrQL/VA8zwo6iJjseXOwT9NjqD9pvwoyBBN+5dUezzjJ6wEvowh5afQlTkg/Ak8DXD1dBcwGlM/rL9ygLm0jmhMuP/osvA42f7nYmVJzJmWn+wJ7qlTKJxTBFdR9VWzdslnWa2ntVs6uD7sEZz31QH9GLEnT6lT1yXSYtF8F6b8JvwrSnknbelSWRl8agX5tAB4FlGxF5CyACwyuntYDrcIbs5roTrSmmrEtvw7pY5auHcL2WtpS1zxIw9u60RoLnPw3a+lqUZ5bkNd/LcOOCLldSLtE8ausjjmJa5JWX6Jfz3AggP8qiJMTP+wOJENhrZZdDEf6KD0eNouBncBGgDfO4wD/v9OfwNWAlzyETLZ1rpeRLU9tEcJs62xV1STZhFYVz5/66MEZsHkWWAuQ15sBHjB+BpwAyL8J2YdK2C/T27owfpXUmHXe4vKraRavcWzr0upLOq96fJ7FxRW6knGuZtyEk8irtkzuE7ka8pJNyOQkNBBYAcwFeKDOm64LcC0g0sJAZwQzgWEaIecg3kdLO0X/gPItgFxy8t8PLAU+AI4D+qoEyVRJWL/K8piTuABZ9SWeNX0NbPND0oUw+g1QT3J7yOXZG4CXvIZMluOsqN748CCMuhGAlxRl5TQfJHArZudXpX9CHg9m3aQvMmjbCPDC8mHAyZ+T03rAhOxDJWxjuoHKTPhVEmPWh5qVlVMWfEnnVcV5zsTtHH0jMdmDlujUnwAdrVY3ITwC6K8RX0eandPBcsRhm542twNOEpcTObWVFt1kdIQ8cYIbZ3VqjKWbZaWjBpwg2YaJySlqX1g+yJi5Utf9yivuxldcfjUFfSOvB4A0SBBeb0WHvbi053VyGeDp0O8CJrrkt37055YfRn8RCvWxCk5DyMPZbsA1wBrgb0DJBkT+UQkrvBThdcB7ALeHuuzWEwWPq4PPRvCwzOJilBWuMsQNn2w9gLTwHmTMH6Pf233ysMWnnSmzhVbf+GBJgwTh9Wd0eJHPTp+A3TEH25OgewdYDCxwyI9N9TBq5lNBbefYEJ/s1D3CRBUpyrauCg2e2e2QexDgxH+eZvkV4jwg76Dp8hKtxZjjWjml6ZokzSvPSJcAzzuQULbKYsdMi5qF52gVj7Ti/FBxAlDWCc1Oov4Y4KFyd2AF8L1VpBdCrjqbAOaNBfIkRRxzEtcvSV7bYkDzAZ5bcxGiy1QkyhYvpienjmjgJoB7ST7FlQxBhOdN3NrdYsURGJNBVk08MC2CqAfAUm2w11txTlZvAzz3y5PUYsxF8KskeZ0Nh7wb6AesAdZa2IFwLvAmEJvwtSC3b8/YWuDTnPvP5YB+IG4za04G2dYNQInVAM+t2C7fVHEfOxzIs3DM3Mt30wbJhwI5+BVo0PR5iSY55iL5VVK88vyZ/umGlbVy1FPRcG+fjXOfz1fjPX3ai1mJgXpE83jeVBphZayIY65kwbxGeDXPqdQoDAgDwoAwIAwIA8KAMCAMCAPCgDAgDAgDwoAwIAwIA8KAMCAMCAPCgDAgDGSEgf8BjA+ia1bX6bQAAAAASUVORK5CYII=" width="147.5" height="20" style="width: 147.5px; height: 20px;"></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="">That is, each new term is the sum of the three previous terms.</span></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="">If the sequence starts with 0, 1, 1, the first 10 Tribonacci numbers are: 0, 1, 1, 2, 4, 7, 13, 24, 44, 81.</span></span></div><div style="block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="">If the sequence instead starts with 2, 3, 7, the first 15 Tribonacci numbers are: 2, 3, 7, 12, 22, 41, 75, 138, 254, 467, 859, 1580, 2906, 5345, 9831.</span></span></div><div style="block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="">Given a vector of three numbers, </span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="font-family: Menlo, Monaco, Consolas, &quot;Courier New&quot;, monospace; ">Tstart</span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="">, and an integer </span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="font-style: italic; ">n</span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style=""> (&gt; 3), return an </span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="font-style: italic; ">n</span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="">-element vector of the first n Tribonacci numbers starting with </span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="font-family: Menlo, Monaco, Consolas, &quot;Courier New&quot;, monospace; ">Tstart</span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="">.</span></span></div><div style="background-color: rgb(247, 247, 247); block-size: 60px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; "><div style="background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; white-space: nowrap; "><span style="block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; tab-size: 4; white-space: pre; margin-right: 45px; "><span style="margin-inline-end: 0px; margin-right: 0px; ">T = tribo([2 3 7],15)</span></span></div><div style="background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; white-space: nowrap; "><span style="block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; tab-size: 4; white-space: pre; margin-right: 45px; "><span style="margin-inline-end: 0px; margin-right: 0px; ">    T = </span></span></div><div style="background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; white-space: nowrap; "><span style="block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; tab-size: 4; white-space: pre; margin-right: 45px; "><span style="margin-inline-end: 0px; margin-right: 0px; ">    2 3 7 12 22 41 75 138 254 467 859 1580 2906 5345 9831</span></span></div></div></div></div>

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Marco Riani on 15 Mar 2023

I think it is important to specify that the output must be a row vector

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Problem 55985. Generate Tribonacci Sequence

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