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A135099 a(1)=1, a(n) = a(n-1) + n^5 if n odd, a(n) = a(n-1) + n^3 if n is even.

%I A135099 #24 Jan 02 2024 08:56:57
%S A135099 1,9,252,316,3441,3657,20464,20976,80025,81025,242076,243804,615097,
%T A135099 617841,1377216,1381312,2801169,2807001,5283100,5291100,9375201,
%U A135099 9385849,15822192,15836016,25601641,25619217,39968124,39990076,60501225
%N A135099 a(1)=1, a(n) = a(n-1) + n^5 if n odd, a(n) = a(n-1) + n^3 if n is even.
%H A135099 G. C. Greubel, <a href="/A135099/b135099.txt">Table of n, a(n) for n = 1..1000</a>
%H A135099 <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 A135099 G.f.: -x*(1 + 8*x + 237*x^2 + 16*x^3 + 1682*x^4 - 48*x^5 + 1682*x^6 + 16*x^7 + 237*x^8 + 8*x^9 + x^ 10)/((1+x)^6 * (x-1)^7). - _R. J. Mathar_, Feb 22 2009
%F A135099 E.g.f.: (1/48)*( (-9 - 18*x - 306*x^2 + 468*x^3 - 150*x^4 + 12*x^5)*exp(-x) + (9 + 48*x + 456*x^2 + 768*x^3 + 396*x^4 + 72*x^5 + 4*x^6)*exp(x) ). - _G. C. Greubel_, Sep 23 2016
%t A135099 a = {}; r = 5; 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
%t A135099 Table[(1/48)*(9*(1 - (-1)^n) + 4*n^2*(n + 1)^2*(n^2 + n + 1) - 6*(-1)^n*n^2*(n + 2)*(2*n^2 + n - 4)), {n, 1, 50}] (* _G. C. Greubel_, Sep 23 2016 *)
%t A135099 nxt[{n_,a_}]:={n+1,If[EvenQ[n],a+(n+1)^5,a+(n+1)^3]}; NestList[nxt,{1,1},30][[All,2]] (* or *) LinearRecurrence[{1,6,-6,-15,15,20,-20,-15,15,6,-6,-1,1},{1,9,252,316,3441,3657,20464,20976,80025,81025,242076,243804,615097},30] (* _Harvey P. Dale_, Oct 02 2022 *)
%o A135099 (PARI) for(n=1,50, print1((1/48)*(9*(1-(-1)^n) +4*n^2*(n+1)^2*(n^2 +n +1) -6*(-1)^n*n^2*(n+2)*(2*n^2 +n-4)), ", ")) \\ _G. C. Greubel_, Jul 05 2018
%o A135099 (Magma) [(1/48)*(9*(1-(-1)^n) +4*n^2*(n+1)^2*(n^2 +n+1) -6*(-1)^n*n^2*(n + 2)*(2*n^2 +n-4)): n in [1..50]]; // _G. C. Greubel_, Jul 05 2018
%Y A135099 Cf. A000027, A000217, A000330, A000537, A000538, A000539, A136047, A140113.
%K A135099 nonn
%O A135099 1,2
%A A135099 _Artur Jasinski_, May 12 2008