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.

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

Harvey P. Dale, Table of n, a(n) for n = 1..1000

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 *)

Crossrefs

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

Sequence in context: A020260 A345500 A345501 * A223733 A083883 A039326

Adjacent sequences: A140144 A140145 A140146 * A140148 A140149 A140150

Keyword

nonn

Author

Artur Jasinski, May 12 2008

Status

approved