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A140159 a(1)=1, a(n) = a(n-1) + n^4 if n odd, a(n) = a(n-1) + n^2 if n is even.

%I A140159 #16 Jan 02 2024 09:02:04
%S A140159 1,5,86,102,727,763,3164,3228,9789,9889,24530,24674,53235,53431,
%T A140159 104056,104312,187833,188157,318478,318878,513359,513843,793684,
%U A140159 794260,1184885,1185561,1717002,1717786,2425067,2425967,3349488,3350512,4536433
%N A140159 a(1)=1, a(n) = a(n-1) + n^4 if n odd, a(n) = a(n-1) + n^2 if n is even.
%H A140159 Harvey P. Dale, <a href="/A140159/b140159.txt">Table of n, a(n) for n = 1..1000</a>
%H A140159 <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 A140159 G.f.: x*(1+4*x+76*x^2-4*x^3+230*x^4-4*x^5+76*x^6+4*x^7+x^8)/((1+x)^5*(x-1)^6). - _R. J. Mathar_, Feb 22 2009
%t A140159 a = {}; r = 4; s = 2; 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 A140159 nxt[{n_,a_}]:={n+1,If[EvenQ[n],a+(n+1)^4,a+(n+1)^2]}; NestList[nxt, {1, 1}, 40][[All, 2]] (* _Harvey P. Dale_, Sep 21 2016 *)
%t A140159 LinearRecurrence[{1,5,-5,-10,10,10,-10,-5,5,1,-1}, {1, 5, 86, 102, 727, 763, 3164, 3228, 9789, 9889, 24530}, 50] (* or *) Table[(1/60)*(n +n^2)* (4 + 30*(-1)^n + (11 -15*(-1)^n)*n + (9 -15*(-1)^n)*n^2 + 6*n^3), {n,1, 50}] (* _G. C. Greubel_, Jul 05 2018 *)
%o A140159 (PARI) for(n=1,50, print1((1/60)*(n +n^2)* (4 + 30*(-1)^n + (11 -15*(-1)^n)*n + (9 -15*(-1)^n)*n^2 + 6*n^3), ", ")) \\ _G. C. Greubel_, Jul 05 2018
%o A140159 (Magma) [(1/60)*(n +n^2)* (4 + 30*(-1)^n + (11 -15*(-1)^n)*n + (9 -15*(-1)^n)*n^2 + 6*n^3): n in [1..50]]; // _G. C. Greubel_, Jul 05 2018
%Y A140159 Cf. A000027, A000217, A000330, A000537, A000538, A000539, A136047, A140113.
%K A140159 nonn
%O A140159 1,2
%A A140159 _Artur Jasinski_, May 12 2008