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A140157 a(1)=1, a(n) = a(n-1) + n^4 if n odd, a(n) = a(n-1) + n^0 if n is even.

%I A140157 #14 Jan 02 2024 09:01:57
%S A140157 1,2,83,84,709,710,3111,3112,9673,9674,24315,24316,52877,52878,103503,
%T A140157 103504,187025,187026,317347,317348,511829,511830,791671,791672,
%U A140157 1182297,1182298,1713739,1713740,2421021,2421022,3344543,3344544,4530465
%N A140157 a(1)=1, a(n) = a(n-1) + n^4 if n odd, a(n) = a(n-1) + n^0 if n is even.
%H A140157 G. C. Greubel, <a href="/A140157/b140157.txt">Table of n, a(n) for n = 1..1000</a>
%H A140157 <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 A140157 G.f.: x*(1 + x + 76*x^2 - 4*x^3 + 230*x^4 + 6*x^5 + 76*x^6 - 4*x^7 + x^8 + x^9)/((1+x)^5*(x-1)^6). - _R. J. Mathar_, Feb 22 2009
%t A140157 a = {}; r = 4; s = 0; 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 A140157 LinearRecurrence[{1,5,-5,-10,10,10,-10,-5,5,1,-1}, {1, 2, 83, 84, 709, 710, 3111, 3112, 9673, 9674, 24315}, 50] (* or *) Table[(1/60)*(15*(-1 + (-1)^n) + (29 +15*(-1)^n)*n + 10*(1 -3*(-1)^n)*n^3 + 15*(1 -(-1)^n)*n^4 + 6*n^5), {n,1,50}] (* _G. C. Greubel_, Jul 05 2018 *)
%o A140157 (PARI) for(n=1,50, print1((1/60)*(15*(-1 + (-1)^n) + (29 +15*(-1)^n)*n + 10*(1 -3*(-1)^n)*n^3 + 15*(1 -(-1)^n)*n^4 + 6*n^5), ", ")) \\ _G. C. Greubel_, Jul 05 2018
%o A140157 (Magma) [(1/60)*(15*(-1 + (-1)^n) + (29 +15*(-1)^n)*n + 10*(1 -3*(-1)^n)*n^3 + 15*(1 -(-1)^n)*n^4 + 6*n^5): n in [1..50]]; // _G. C. Greubel_, Jul 05 2018
%Y A140157 Cf. A000027, A000217, A000330, A000537, A000538, A000539, A136047, A140113.
%K A140157 nonn
%O A140157 1,2
%A A140157 _Artur Jasinski_, May 12 2008