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%I #18 Jan 02 2024 09:02:25
%S 1,33,114,1138,1763,9539,11940,44708,51269,151269,165910,414742,
%T 443303,981127,1031752,2080328,2163849,4053417,4183738,7383738,
%U 7578219,12731851,13011692,20974316,21364941,33246317,33777758,50988126
%N a(1)=1, a(n) = a(n-1) + n^4 if n odd, a(n) = a(n-1) + n^5 if n is even.
%H Harvey P. Dale, <a href="/A140161/b140161.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (1,6,-6,-15,15,20,-20,-15,15,6,-6, -1,1).
%F G.f.: x*(-1 - 32*x - 75*x^2 - 832*x^3 - 154*x^4 - 2112*x^5 + 154*x^6 - 832*x^7 + 75*x^8 - 32*x^9 + x^10)/((1+x)^6*(x-1)^7). - _R. J. Mathar_, Feb 22 2009
%t a = {}; r = 4; 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 *)
%t next[{a_,b_}]:={a+1,If[OddQ[a+1],b+(a+1)^4,b+(a+1)^5]}; Transpose[ NestList[ next[#]&,{1,1},30]][[2]] (* _Harvey P. Dale_, Nov 23 2011 *)
%t Table[(1/120)*(15*(-1 +(-1)^n) - 2*(1 -15*(-1)^n)*n - 5*(1 +15*(-1)^n)*n^2 + 20*(1 -3*(-1)^n)*n^3 + (55 + 45*(-1)^n)*n^4 + (42 +30*(-1)^n)*n^5 + 10*n^6), {n,1,50}] (* _G. C. Greubel_, Jul 05 2018 *)
%o (PARI) for(n=1, 50, print1((1/120)*(15*(-1 +(-1)^n) - 2*(1 -15*(-1)^n)*n - 5*(1 +15*(-1)^n)*n^2 + 20*(1 -3*(-1)^n)*n^3 + (55 + 45*(-1)^n)*n^4 + (42 +30*(-1)^n)*n^5 + 10*n^6), ", ")) \\ _G. C. Greubel_, Jul 05 2018
%o (Magma) [(1/120)*(15*(-1 +(-1)^n) - 2*(1 -15*(-1)^n)*n - 5*(1 +15*(-1)^n)*n^2 + 20*(1 -3*(-1)^n)*n^3 + (55 + 45*(-1)^n)*n^4 + (42 +30*(-1)^n)*n^5 + 10*n^6): n in [1..50]]; // _G. C. Greubel_, Jul 05 2018
%Y Cf. A000027, A000217, A000330, A000537, A000538, A000539, A136047, A140113.
%K nonn
%O 1,2
%A _Artur Jasinski_, May 12 2008
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