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A140156 a(1)=1, a(n) = a(n-1) + n^3 if n odd, a(n) = a(n-1) + n^5 if n is even.

%I A140156 #28 Jan 02 2024 09:01:54
%S A140156 1,33,60,1084,1209,8985,9328,42096,42825,142825,144156,392988,395185,
%T A140156 933009,936384,1984960,1989873,3879441,3886300,7086300,7095561,
%U A140156 12249193,12261360,20223984,20239609,32120985,32140668,49351036,49375425
%N A140156 a(1)=1, a(n) = a(n-1) + n^3 if n odd, a(n) = a(n-1) + n^5 if n is even.
%H A140156 Harvey P. Dale, <a href="/A140156/b140156.txt">Table of n, a(n) for n = 1..1000</a>
%H A140156 <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 A140156 G.f.: -x*(1 + 32*x + 21*x^2 + 832*x^3 - 22*x^4 + 2112*x^5 - 22*x^6 + 832*x^7 + 21*x^8 + 32*x^9 + x^10)/((1+x)^6*(x-1)^7). - _R. J. Mathar_, Feb 22 2009
%t A140156 a = {}; r = 3; 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 A140156 nxt[{n_,a_}]:={n+1,If[EvenQ[n],a+(n+1)^3,a+(n+1)^5]}; Transpose[ NestList[ nxt,{1,1},30]][[2]] (* or *) LinearRecurrence[ {1,6,-6,-15, 15,20,-20,-15,15,6,-6,-1,1},{1,33,60,1084,1209,8985,9328, 42096, 42825, 142825,144156, 392988,395185},40] (* _Harvey P. Dale_, Aug 27 2013 *)
%t A140156 Table[(1/48)*(9*(-1 +(-1)^n) + 4*(1 -12(-1)^n)*n^2 + 12*(1 -(-1)^n)*n^3 + (16 + 30*(-1)^n)*n^4 + 12*(1 +(-1)^n)*n^5 + 4*n^6), {n, 1, 50}] (* _G. C. Greubel_, Jul 05 2018 *)
%o A140156 (PARI) for(n=1, 50, print1((1/48)*(9*(-1 +(-1)^n) + 4*(1 -12(-1)^n)*n^2 + 12*(1 -(-1)^n)*n^3 + (16 + 30*(-1)^n)*n^4 + 12*(1 +(-1)^n)*n^5 + 4*n^6), ", ")) \\ _G. C. Greubel_, Jul 05 2018
%o A140156 (Magma) [(1/48)*(9*(-1 +(-1)^n) + 4*(1 -12(-1)^n)*n^2 + 12*(1 -(-1)^n)*n^3 + (16 + 30*(-1)^n)*n^4 + 12*(1 +(-1)^n)*n^5 + 4*n^6): n in [1..50]]; // _G. C. Greubel_, Jul 05 2018
%Y A140156 Cf. A000027, A000217, A000330, A000537, A000538, A000539, A136047, A140113.
%K A140156 nonn,easy
%O A140156 1,2
%A A140156 _Artur Jasinski_, May 12 2008