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 A145285 a(n) is the number of monomials in the n-th power of polynomial x^4-x^3-x^2-x-1. 1
 5, 8, 12, 16, 20, 25, 28, 32, 37, 41, 45, 49, 53, 57, 61, 65, 69, 73, 77, 81, 85, 89, 93, 97, 101, 105, 109, 113, 117, 121, 125, 129, 133, 137, 141, 145, 149, 153, 157, 161, 165, 169, 173, 177, 181, 185, 189, 193, 197, 201, 205, 209, 213, 217, 221, 225, 229, 233 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS a(n)=Length[(x^4-x^3-x^2-x-1)^n]. LINKS Index entries for linear recurrences with constant coefficients, signature (2,-1). FORMULA From Chai Wah Wu, Sep 24 2020: (Start) a(n) = 2*a(n-1) - a(n-2) for n > 10. G.f.: x*(-x^9 + x^8 + x^7 - 2*x^6 + x^5 + x^2 - 2*x + 5)/(x - 1)^2. (End) MATHEMATICA a = {}; k = x^4 - x^3 - x^2- x - 1; m = k; Do[AppendTo[a, Length[m]]; m = Expand[m*k], {n, 1, 100}]; a (*Artur Jasinski*) PROG (Python) from sympy import expand from sympy.abc import x def A145285(n):     return len(expand((x**4-x**3-x**2-x-1)**n).as_terms()[0]) # Chai Wah Wu, Sep 24 2020 CROSSREFS Sequence in context: A287114 A314408 A190708 * A314409 A314410 A222802 Adjacent sequences:  A145282 A145283 A145284 * A145286 A145287 A145288 KEYWORD nonn AUTHOR Artur Jasinski, Oct 06 2008 STATUS approved

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Last modified December 5 15:06 EST 2021. Contains 349557 sequences. (Running on oeis4.)