Problem 44466. The twelve days of Christmas

Created by David Verrelli

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Traditionally there are twelve days of Christmas to celebrate ("Twelvetide"), typically starting with Christmas Day (25 December) as the "First Day of Christmas" and finishing on the 5th of January.In the traditional Christmas carol, helpfully entitled <a href = "http://christmas-lyrics.com/christmas-carols-lyrics/the-twelve-days-of-christmas-lyrics/">The Twelve Days of Christmas</a>, the singer recounts receiving gifts on each day, sent to them by their True Love.On the first day, they receive one gift (1 × "partridge in a pear tree").On the second day they receive two new gifts (2 × "turtle doves") plus a repeat of each gift corresponding to the previous days — in this case meaning plus one repeat gift (1 × "partridge in a pear tree"). Therefore they have accumulated a total of four gifts: one from the first day, and three from the second day.On the third day they receive three new gifts (3 × "French hens") plus a repeat of each gift corresponding to the previous days — in this case meaning plus three repeat gifts (1 × "partridge in a pear tree" and 2 × "turtle doves"). By now they have accumulated a total of ten gifts: one from the first day, three from the second day, and six from the third day.This continues until the twelfth day (the last day of Christmas).For this problem you must calculate the cumulative total of all gifts received up to the specified day that is provided as input. (Day 1 is the 25th of December, day 2 is the 26th of December, and so on.)EXAMPLE<pre> day = 2
 accumulatedGifts = 4</pre>

Traditionally there are twelve days of Christmas to celebrate ("Twelvetide"), typically starting with Christmas Day (25 December) as the "First Day of Christmas" and finishing on the 5th of January.

In the traditional Christmas carol, helpfully entitled <http://christmas-lyrics.com/christmas-carols-lyrics/the-twelve-days-of-christmas-lyrics/ _The Twelve Days of Christmas_>, the singer recounts receiving gifts on each day, sent to them by their True Love.

On the *first* day, they receive *one* gift (1 × "partridge in a pear tree").

On the *second* day they receive *two* _new_ gifts (2 × "turtle doves") *plus* a repeat of each gift corresponding to the previous days — in this case meaning plus *one* _repeat_ gift (1 × "partridge in a pear tree").  Therefore they have _accumulated_ a total of four gifts:  one from the first day, and three from the second day.

On the *third* day they receive *three* _new_ gifts (3 × "French hens") *plus* a repeat of each gift corresponding to the previous days — in this case meaning plus *three* _repeat_ gifts (1 × "partridge in a pear tree" and 2 × "turtle doves").  By now they have _accumulated_ a total of ten gifts:  one from the first day, three from the second day, and six from the third day.

This continues until the twelfth day (the _last_ day of Christmas).

For this problem you must calculate the cumulative total of all gifts received up to the specified day that is provided as input.  (Day 1 is the 25th of December, day 2 is the 26th of December, and so on.)

EXAMPLE

day = 2
 accumulatedGifts = 4

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Problem 44466. The twelve days of Christmas

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