OFFSET
1,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1, 6, -6, -15, 15, 20, -20, -15, 15, 6, -6, -1, 1).
FORMULA
G.f.: -x*(1 + 8*x + 237*x^2 + 16*x^3 + 1682*x^4 - 48*x^5 + 1682*x^6 + 16*x^7 + 237*x^8 + 8*x^9 + x^ 10)/((1+x)^6 * (x-1)^7). - R. J. Mathar, Feb 22 2009
E.g.f.: (1/48)*( (-9 - 18*x - 306*x^2 + 468*x^3 - 150*x^4 + 12*x^5)*exp(-x) + (9 + 48*x + 456*x^2 + 768*x^3 + 396*x^4 + 72*x^5 + 4*x^6)*exp(x) ). - G. C. Greubel, Sep 23 2016
MATHEMATICA
a = {}; r = 5; s = 3; 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
Table[(1/48)*(9*(1 - (-1)^n) + 4*n^2*(n + 1)^2*(n^2 + n + 1) - 6*(-1)^n*n^2*(n + 2)*(2*n^2 + n - 4)), {n, 1, 50}] (* G. C. Greubel, Sep 23 2016 *)
nxt[{n_, a_}]:={n+1, If[EvenQ[n], a+(n+1)^5, a+(n+1)^3]}; NestList[nxt, {1, 1}, 30][[All, 2]] (* or *) LinearRecurrence[{1, 6, -6, -15, 15, 20, -20, -15, 15, 6, -6, -1, 1}, {1, 9, 252, 316, 3441, 3657, 20464, 20976, 80025, 81025, 242076, 243804, 615097}, 30] (* Harvey P. Dale, Oct 02 2022 *)
PROG
(PARI) for(n=1, 50, print1((1/48)*(9*(1-(-1)^n) +4*n^2*(n+1)^2*(n^2 +n +1) -6*(-1)^n*n^2*(n+2)*(2*n^2 +n-4)), ", ")) \\ G. C. Greubel, Jul 05 2018
(Magma) [(1/48)*(9*(1-(-1)^n) +4*n^2*(n+1)^2*(n^2 +n+1) -6*(-1)^n*n^2*(n + 2)*(2*n^2 +n-4)): n in [1..50]]; // G. C. Greubel, Jul 05 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Artur Jasinski, May 12 2008
STATUS
approved