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A135214
a(1)=1, a(n) = a(n-1) + n^5 if n odd, a(n) = a(n-1) + n^4 if n is even.
2
1, 17, 260, 516, 3641, 4937, 21744, 25840, 84889, 94889, 255940, 276676, 647969, 686385, 1445760, 1511296, 2931153, 3036129, 5512228, 5672228, 9756329, 9990585, 16426928, 16758704, 26524329, 26981305, 41330212, 41944868, 62456017
OFFSET
1,2
LINKS
Index entries for linear recurrences with constant coefficients, signature (1,6,-6,-15,15,20,-20,-15,15,6,-6,-1,1).
FORMULA
From R. J. Mathar, May 17 2008: (Start)
O.g.f.: x*(1 + x^2)*(x^8 - 16*x^7 + 236*x^6 - 144*x^5 + 1446*x^4 + 144*x^3 + 236*x^2 + 16*x + 1)/((1-x)^7 *(1+x)^6).
a(2*n-1) = n*(-8 + 80*n^2 + 48*n^4 + 80*n^5 + 35*n - 220*n^3)/15.
a(2*n) = n*(-8 + 80*n^2 + 48*n^4 + 80*n^5 + 35*n + 20*n^3)/15 . (End)
MATHEMATICA
a = {}; r = 5; s = 4; Do[k = 0; Do[k = k + (Sin[Pi m/2]^2) m^r + (Cos[Pi m/2]^2) m^s, {m, 1, n}]; AppendTo[a, k], {n, 1, 100}]; a
LinearRecurrence[{1, 6, -6, -15, 15, 20, -20, -15, 15, 6, -6, -1, 1}, {1, 17, 260, 516, 3641, 4937, 21744, 25840, 84889, 94889, 255940, 276676, 647969}, 50] (* G. C. Greubel, Oct 04 2016 *)
PROG
(PARI) x='x+O('x^50); Vec(x*(1 + x^2)*(x^8 - 16*x^7 + 236*x^6 - 144*x^5 + 1446*x^4 + 144*x^3 + 236*x^2 + 16*x + 1)/((1-x)^7 *(1+x)^6)) \\ G. C. Greubel, Jul 04 2018
(Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(x*(1 + x^2)*(x^8 - 16*x^7 + 236*x^6 - 144*x^5 + 1446*x^4 + 144*x^3 + 236*x^2 + 16*x + 1)/((1-x)^7 *(1+x)^6))) // G. C. Greubel, Jul 04 2018
KEYWORD
nonn
AUTHOR
Artur Jasinski, May 12 2008
STATUS
approved