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A140158 a(1)=1, a(n) = a(n-1) + n^4 if n odd, a(n) = a(n-1) + n^1 if n is even.

%I A140158 #16 Dec 28 2024 18:18:21
%S A140158 1,3,84,88,713,719,3120,3128,9689,9699,24340,24352,52913,52927,103552,
%T A140158 103568,187089,187107,317428,317448,511929,511951,791792,791816,
%U A140158 1182441,1182467,1713908,1713936,2421217,2421247,3344768,3344800,4530721
%N A140158 a(1)=1, a(n) = a(n-1) + n^4 if n odd, a(n) = a(n-1) + n^1 if n is even.
%H A140158 G. C. Greubel, <a href="/A140158/b140158.txt">Table of n, a(n) for n = 1..1000</a>
%H A140158 <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 A140158 G.f.: x*(1 + 2*x + 76*x^2 - 6*x^3 + 230*x^4 + 6*x^5 + 76*x^6 - 2*x^7 + x^8)/((1+x)^5*(x-1)^6). - _R. J. Mathar_, Feb 22 2009
%t A140158 a = {}; r = 4; s = 1; 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 A140158 LinearRecurrence[{1,5,-5,-10,10,10,-10,-5,5,1,-1}, {1, 3, 84, 88, 713, 719, 3120, 3128, 9689, 9699, 24340}, 50] (* or *) Table[(1/120)*(15*(-1 +(-1)^n) + (28 + 60*(-1)^n)*n + 30*n^2 + 20*(1 - 3*(-1)^n)*n^3 + 30*(1 -(-1)^n)*n^4 + 12*n^5), {n,1,50}] (* _G. C. Greubel_, Jul 05 2018 *)
%t A140158 nxt[{n_,a_}]:={n+1,If[EvenQ[n],a+(n+1)^4,a+n+1]}; NestList[nxt,{1,1},40][[;;,2]] (* _Harvey P. Dale_, Dec 28 2024 *)
%o A140158 (PARI) for(n=1,50, print1((1/120)*(15*(-1 +(-1)^n) + (28 + 60*(-1)^n)*n + 30*n^2 + 20*(1 - 3*(-1)^n)*n^3 + 30*(1 -(-1)^n)*n^4 + 12*n^5), ", ")) \\ _G. C. Greubel_, Jul 05 2018
%o A140158 (Magma) [(1/120)*(15*(-1 +(-1)^n) + (28 + 60*(-1)^n)*n + 30*n^2 + 20*(1 - 3*(-1)^n)*n^3 + 30*(1 -(-1)^n)*n^4 + 12*n^5): n in [1..50]]; // _G. C. Greubel_, Jul 05 2018
%Y A140158 Cf. A000027, A000217, A000330, A000537, A000538, A000539, A136047, A140113.
%K A140158 nonn
%O A140158 1,2
%A A140158 _Artur Jasinski_, May 12 2008