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A140147
a(1)=1, a(n)=a(n-1)+n^1 if n odd, a(n)=a(n-1)+ n^5 if n is even.
2
1, 33, 36, 1060, 1065, 8841, 8848, 41616, 41625, 141625, 141636, 390468, 390481, 928305, 928320, 1976896, 1976913, 3866481, 3866500, 7066500, 7066521, 12220153, 12220176, 20182800, 20182825, 32064201, 32064228, 49274596, 49274625
OFFSET
1,2
LINKS
FORMULA
G.f.: -x*(1+32*x-3*x^2+832*x^3+2*x^4+2112*x^5+2*x^6+832*x^7-3*x^8+32*x^9+x^10)/ ((1+x)^6*(x-1)^7). [From R. J. Mathar, Feb 22 2009]
MATHEMATICA
a = {}; r = 1; s = 5; 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_}]:=If[OddQ[n+1], {n+1, a+n+1}, {n+1, a+(n+1)^5}]; Transpose[ NestList[ nxt, {1, 1}, 30]][[2]] (* Harvey P. Dale, Jun 27 2012 *)
KEYWORD
nonn
AUTHOR
Artur Jasinski, May 12 2008
STATUS
approved