A140160 a(1)=1, a(n) = a(n-1) + n^4 if n odd, a(n) = a(n-1) + n^3 if n is even.

1, 9, 90, 154, 779, 995, 3396, 3908, 10469, 11469, 26110, 27838, 56399, 59143, 109768, 113864, 197385, 203217, 333538, 341538, 536019, 546667, 826508, 840332, 1230957, 1248533, 1779974, 1801926, 2509207, 2536207, 3459728, 3492496

Offset: 1

Author

Artur Jasinski, May 12 2008

Keywords

• nonn

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (1,5,-5,-10,10,10,-10,-5,5,1,-1).

Crossrefs

Cf. A000027, A000217, A000330, A000537, A000538, A000539, A136047, A140113.

Programs

Magma

[(1/240)*(15*(1 -(-1)^n) - 4*(1 - 15*(-1)^n)*n + 30*(1 + 3(-1)^n)*n^2 + 20*(5 - 3*(-1)^n)*n^3 + 30*(3 - 2*(-1)^n)*n^4 + 24*n^5): n in [1..50]]; // G. C. Greubel, Jul 05 2018

Mathematica

a = {}; r = 4; 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 (* Artur Jasinski *)
nxt[{n_,a_}]:={n+1,If[EvenQ[n],a+(n+1)^4,a+(n+1)^3]}; NestList[nxt,{1,1},40][[All,2]] (* or *) LinearRecurrence[{1,5,-5,-10,10,10,-10,-5,5,1,-1},{1,9,90,154,779,995,3396,3908,10469,11469,26110},40] (* Harvey P. Dale, Oct 05 2016 *)
Table[(1/240)*(15*(1 -(-1)^n) - 4*(1 - 15*(-1)^n)*n + 30*(1 + 3(-1)^n)*n^2 + 20*(5 - 3*(-1)^n)*n^3 + 30*(3 - 2*(-1)^n)*n^4 + 24*n^5), {n,1,50}] (* G. C. Greubel, Jul 05 2018 *)

PARI

for(n=1,50, print1((1/240)*(15*(1 -(-1)^n) - 4*(1 - 15*(-1)^n)*n + 30*(1 + 3(-1)^n)*n^2 + 20*(5 - 3*(-1)^n)*n^3 + 30*(3 - 2*(-1)^n)*n^4 + 24*n^5), ", ")) \\ G. C. Greubel, Jul 05 2018

Formula

G.f.: x*(1 + 8*x + 76*x^2 + 24*x^3 + 230*x^4 - 24*x^5 + 76*x^6 - 8*x^7 + x^8)/((1+x)^5*(x-1)^6). - R. J. Mathar, Feb 22 2009