%I #12 Jan 02 2024 09:01:09

%S 1,17,20,276,281,1577,1584,5680,5689,15689,15700,36436,36449,74865,

%T 74880,140416,140433,245409,245428,405428,405449,639705,639728,971504,

%U 971529,1428505,1428532,2043188,2043217,2853217,2853248,3901824,3901857

%N a(1)=1, a(n)=a(n-1)+n^1 if n odd, a(n)=a(n-1)+ n^4 if n is even.

%H Harvey P. Dale, <a href="/A140146/b140146.txt">Table of n, a(n) for n = 1..1000</a>

%F G.f.: -x*(x^2+1)*(x^6-16*x^5-3*x^4-160*x^3+3*x^2-16*x-1)/((1+x)^5*(x-1)^6). [From _R. J. Mathar_, Feb 22 2009]

%t a = {}; r = 1; s = 4; 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*)

%t nxt[{n_,a_}]:={n+1,If[OddQ[n+1],a+n+1,a+(n+1)^4]}; Transpose[NestList[nxt,{1,1},40]][[2]] (* _Harvey P. Dale_, Mar 19 2013 *)

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

%K nonn

%O 1,2

%A _Artur Jasinski_, May 12 2008