A140152 a(1)=1, a(n)=a(n-1)+n^3 if n odd, a(n)=a(n-1)+ n^0 if n is even.
1, 2, 29, 30, 155, 156, 499, 500, 1229, 1230, 2561, 2562, 4759, 4760, 8135, 8136, 13049, 13050, 19909, 19910, 29171, 29172, 41339, 41340, 56965, 56966, 76649, 76650, 101039, 101040, 130831, 130832, 166769, 166770, 209645, 209646, 260299
Offset: 1
Keywords
Programs
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Mathematica
a = {}; r = 3; s = 0; 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[{a_,b_}]:={a+1,If[EvenQ[a],b+(a+1)^3,b+1]}; Transpose[NestList[nxt,{1,1},40]][[2]] (* Harvey P. Dale, Dec 13 2011 *)
Formula
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). G.f.: x*(-1-x-23*x^2+3*x^3-23*x^4-3*x^5-x^6+x^7)/((1+x)^4*(x-1)^5). [R. J. Mathar, Feb 22 2009]