A140149 a(1)=1, a(n)=a(n-1)+n^2 if n odd, a(n)=a(n-1)+ n^3 if n is even.

1, 9, 18, 82, 107, 323, 372, 884, 965, 1965, 2086, 3814, 3983, 6727, 6952, 11048, 11337, 17169, 17530, 25530, 25971, 36619, 37148, 50972, 51597, 69173, 69902, 91854, 92695, 119695, 120656, 153424, 154513, 193817, 195042, 241698, 243067

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 (1,4,-4,-6,6,4,-4,-1,1).

Crossrefs

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

Programs

Mathematica

a = {}; r = 2; 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)^2,a+(n+1)^3]}; NestList[nxt,{1,1},40][[;;,2]] (* or *) LinearRecurrence[{1,4,-4,-6,6,4,-4,-1,1},{1,9,18,82,107,323,372,884,965},40] (* Harvey P. Dale, May 27 2024 *)

Formula

From R. J. Mathar, Feb 22 2009: (Start)

G.f.: x*(-1-8*x-5*x^2-32*x^3+5*x^4-8*x^5+x^6)/((1+x)^4*(x-1)^5).

a(n) = a(n-1)+4*a(n-2)-4*a(n-3)-6*a(n-4)+6*a(n-5)+4*a(n-6)-4*a(n-7)-a(n-8)+a(n-9). (End)