Are you sure about the first rule? It doesn't seem necessary according to https://oeis.org/A014575.
The problem is really fun.
Since I created the problem series and want the Functions I badge, I thought I'd provide the solution that incorporates vampire_factor and are_fangs. Not a great score, but readable!
Sorry, I mean the Magic Numbers badge.
Program an exclusive OR operation with logical operators
How to subtract?
Return 'on' or 'off'
Sum the numbers on the main diagonal
Number of Even Elements in Fibonacci Sequence
Negation the hard way
Multivariate polynomials - overload multiplication
Product of two multivariate polynomials
Multivariate polynomials - convert monomial form to array
Multivariate polynomials - emulate symbolic form
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