A140150 a(1)=1, a(n)=a(n-1)+n^2 if n odd, a(n)=a(n-1)+ n^4 if n is even.

1, 17, 26, 282, 307, 1603, 1652, 5748, 5829, 15829, 15950, 36686, 36855, 75271, 75496, 141032, 141321, 246297, 246658, 406658, 407099, 641355, 641884, 973660, 974285, 1431261, 1431990, 2046646, 2047487, 2857487, 2858448, 3907024, 3908113

Offset: 1

Author

Artur Jasinski, May 12 2008

Keywords

• nonn

Links

• 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

Mathematica

a = {}; r = 2; 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 (*Artur Jasinski*)
nxt[{n_,a_}]:={n+1,If[EvenQ[n],a+(n+1)^2,a+(n+1)^4]}; NestList[nxt,{1,1},40][[All,2]] (* or *) LinearRecurrence[{1,5,-5,-10,10,10,-10,-5,5,1,-1},{1,17,26,282,307,1603,1652,5748,5829,15829,15950},40] (* Harvey P. Dale, Aug 28 2017 *)

Formula

G.f.: x*(1+16*x+4*x^2+176*x^3-10*x^4+176*x^5+4*x^6+16*x^7+x^8)/((1+x)^5*(x-1)^6). [From R. J. Mathar, Feb 22 2009]