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A140160 a(1)=1, a(n) = a(n-1) + n^4 if n odd, a(n) = a(n-1) + n^3 if n is even.

%I A140160 #18 Jan 02 2024 09:02:21
%S A140160 1,9,90,154,779,995,3396,3908,10469,11469,26110,27838,56399,59143,
%T A140160 109768,113864,197385,203217,333538,341538,536019,546667,826508,
%U A140160 840332,1230957,1248533,1779974,1801926,2509207,2536207,3459728,3492496
%N A140160 a(1)=1, a(n) = a(n-1) + n^4 if n odd, a(n) = a(n-1) + n^3 if n is even.
%H A140160 Harvey P. Dale, <a href="/A140160/b140160.txt">Table of n, a(n) for n = 1..1000</a>
%H A140160 <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (1,5,-5,-10,10,10,-10,-5,5,1,-1).
%F A140160 G.f.: x*(1 + 8*x + 76*x^2 + 24*x^3 + 230*x^4 - 24*x^5 + 76*x^6 - 8*x^7 + x^8)/((1+x)^5*(x-1)^6). - _R. J. Mathar_, Feb 22 2009
%t A140160 a = {}; r = 4; s = 3; 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 A140160 nxt[{n_,a_}]:={n+1,If[EvenQ[n],a+(n+1)^4,a+(n+1)^3]}; NestList[nxt,{1,1},40][[All,2]] (* or *) LinearRecurrence[{1,5,-5,-10,10,10,-10,-5,5,1,-1},{1,9,90,154,779,995,3396,3908,10469,11469,26110},40] (* _Harvey P. Dale_, Oct 05 2016 *)
%t A140160 Table[(1/240)*(15*(1 -(-1)^n) - 4*(1 - 15*(-1)^n)*n + 30*(1 + 3(-1)^n)*n^2 + 20*(5 - 3*(-1)^n)*n^3 + 30*(3 - 2*(-1)^n)*n^4 + 24*n^5), {n,1,50}] (* _G. C. Greubel_, Jul 05 2018 *)
%o A140160 (PARI) for(n=1,50, print1((1/240)*(15*(1 -(-1)^n) - 4*(1 - 15*(-1)^n)*n + 30*(1 + 3(-1)^n)*n^2 + 20*(5 - 3*(-1)^n)*n^3 + 30*(3 - 2*(-1)^n)*n^4 + 24*n^5), ", ")) \\ _G. C. Greubel_, Jul 05 2018
%o A140160 (Magma) [(1/240)*(15*(1 -(-1)^n) - 4*(1 - 15*(-1)^n)*n + 30*(1 + 3(-1)^n)*n^2 + 20*(5 - 3*(-1)^n)*n^3 + 30*(3 - 2*(-1)^n)*n^4 + 24*n^5): n in [1..50]]; // _G. C. Greubel_, Jul 05 2018
%Y A140160 Cf. A000027, A000217, A000330, A000537, A000538, A000539, A136047, A140113.
%K A140160 nonn
%O A140160 1,2
%A A140160 _Artur Jasinski_, May 12 2008