A140145 a(1)=1, a(n)=a(n-1)+n^1 if n odd, a(n)=a(n-1)+ n^3 if n is even.

1, 9, 12, 76, 81, 297, 304, 816, 825, 1825, 1836, 3564, 3577, 6321, 6336, 10432, 10449, 16281, 16300, 24300, 24321, 34969, 34992, 48816, 48841, 66417, 66444, 88396, 88425, 115425, 115456, 148224, 148257, 187561, 187596, 234252, 234289, 289161

Offset: 1

Author

Artur Jasinski, May 12 2008

Keywords

• nonn

Crossrefs

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

Programs

Mathematica

a = {}; r = 1; 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*)

Formula

a(n)=a(n-1)+4a(n-2)-4a(n-3)-6a(n-4)+6a(n-5)+4a(n-6)-4a(n-7)-a(n-8)+a(n-9). G.f.: -x*(1+8*x-x^2+32*x^3-x^4+8*x^5+x^6)/((1+x)^4*(x-1)^5). [From R. J. Mathar, Feb 22 2009]