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A140143 a(1)=1, a(n)=a(n-1)+n^0 if n odd, a(n)=a(n-1)+ n^5 if n is even.

%I A140143 #9 Jan 02 2024 09:00:10
%S A140143 1,33,34,1058,1059,8835,8836,41604,41605,141605,141606,390438,390439,
%T A140143 928263,928264,1976840,1976841,3866409,3866410,7066410,7066411,
%U A140143 12220043,12220044,20182668,20182669,32064045,32064046
%N A140143 a(1)=1, a(n)=a(n-1)+n^0 if n odd, a(n)=a(n-1)+ n^5 if n is even.
%F A140143 a(n)=a(n-1)+6a(n-2)-6a(n-3)-15a(n-4)+15a(n-5)+20a(n-6)-20a(n-7)-15a(n-8)+15a(n-9)+6a(n-10)-6a(n-11)-a(n-12)+a(n-13). G.f.: x*(-1-32*x+5*x^2-832*x^3-10*x^4-2112*x^5+10*x^6-832*x^7-5*x^8-32*x^9+x^10 )/((1+x)^6*(x-1)^7). [From _R. J. Mathar_, Feb 22 2009]
%t A140143 a = {}; r = 0; s = 5; 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*)
%Y A140143 Cf. A000027, A000217, A000330, A000537, A000538, A000539, A136047, A140113.
%K A140143 nonn
%O A140143 1,2
%A A140143 _Artur Jasinski_, May 12 2008, corrected May 17 2008