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A140154 a(1)=1, a(n) = a(n-1) + n^3 if n odd, a(n) = a(n-1) + n^2 if n is even.

%I A140154 #19 Jan 02 2024 09:01:43
%S A140154 1,5,32,48,173,209,552,616,1345,1445,2776,2920,5117,5313,8688,8944,
%T A140154 13857,14181,21040,21440,30701,31185,43352,43928,59553,60229,79912,
%U A140154 80696,105085,105985,135776,136800,172737,173893,216768,218064,268717
%N A140154 a(1)=1, a(n) = a(n-1) + n^3 if n odd, a(n) = a(n-1) + n^2 if n is even.
%H A140154 Muniru A Asiru, <a href="/A140154/b140154.txt">Table of n, a(n) for n = 1..2000</a>
%H A140154 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (1,4,-4,-6,6,4,-4,-1,1).
%F A140154 a(n) = a(n-1) + {[1-(-1)^n]/2}*n^3 + {[1+(-1)^n]/2}*n^2, with a(1)=1.
%F A140154 From _R. J. Mathar_, Feb 22 2009: (Start)
%F A140154 a(n) = a(n-1) + 4*a(n-2) - 4*a(n-3) - 6*a(n-4) + 6*a(n-5) + 4*a(n-6) - 4*a(n-7) - a(n-8) + a(n-9).
%F A140154 G.f.: x*(x^2+1)*(x^4-4*x^3+22*x^2+4*x+1)/((1+x)^4*(1-x)^5). (End)
%p A140154 a:=proc(n) option remember: if n=1 then 1 elif modp(n,2)<>0 then procname(n-1)+n^3 else procname(n-1)+n^2; fi: end; seq(a(n),n=1..40); # _Muniru A Asiru_, Jul 12 2018
%t A140154 a = {}; r = 3; 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 A140154 CoefficientList[Series[x*(x^2+1)*(x^4-4*x^3+22*x^2+4*x+1)/((1+x)^4*(1-x)^5), {x,0,30}], x] (* _G. C. Greubel_, Jul 12 2018 *)
%t A140154 nxt[{n_,a_}]:={n+1,If[EvenQ[n],a+(n+1)^3,a+(n+1)^2]}; NestList[nxt,{1,1},40][[All,2]] (* _Harvey P. Dale_, Aug 05 2019 *)
%o A140154 (PARI) x='x+O('x^30); Vec(x*(x^2+1)*(x^4-4*x^3+22*x^2+4*x+1)/((1+x)^4*(1-x)^5)) \\ _G. C. Greubel_, Jul 12 2018
%o A140154 (Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(x*(x^2+1)*(x^4-4*x^3+22*x^2+4*x+1)/((1+x)^4*(1-x)^5))); // _G. C. Greubel_, Jul 12 2018
%o A140154 (GAP) a:=[1];; for n in [2..40] do a[n]:=a[n-1]+((1-(-1)^n)/2)*n^3+((1+(-1)^n)/2)*n^2; od; a; # _Muniru A Asiru_, Jul 12 2018
%Y A140154 Cf. A000027, A000217, A000330, A000537, A000538, A000539, A136047, A140113.
%K A140154 nonn
%O A140154 1,2
%A A140154 _Artur Jasinski_, May 12 2008