Search: id:A140149
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%I A140149
%S A140149 1,9,18,82,107,323,372,884,965,1965,2086,3814,3983,6727,6952,11048,
%T A140149 11337,17169,17530,25530,25971,36619,37148,50972,51597,69173,69902,
%U A140149 91854,92695,119695,120656,153424,154513,193817,195042,241698,243067
%N A140149 a(1)=1, a(n)=a(n-1)+n^2 if n odd, a(n)=a(n-1)+ n^3 if n is even.
%F A140149 a(n)=a(n-1)+{[1-(-1)^n]/2}*n^2+{[1+(-1)^n]/2}*n^3, with a(1)=1 a(n)= 
               (1/16)-(1/4)*(-1)^n*n-(1/16)*(-1)^n+(1/4)*(-1)^n*n^3+(5/12)*n^3+(1/
               8)*(-1)^n*n^2+(3/8)*n^2+(1 /12)*n+(1/8)*n^4, with n>=1 - Paolo P. 
               Lava (ppl(AT)spl.at), Jun 06 2008
%F A140149 a(n)=a(n-1)+4a(n-2)-4a(n-3)-6a(n-4)+6a(n-5)+4a(n-6)-4a(n-7)-a(n-8)+a(n-9). 
               G.f.: x*(-1-8*x-5*x^2-32*x^3+5*x^4-8*x^5+x^6)/((1+x)^4*(x-1)^5). 
               [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 22 2009]
%t A140149 a = {}; r = 2; 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 (*Artur 
               Jasinski*)
%Y A140149 Cf. A000027, A000217, A000330, A000537, A000538, A000539, A136047, A140113.
%Y A140149 Sequence in context: A022669 A107313 A166640 this_sequence A066711 A033651 
               A050250
%Y A140149 Adjacent sequences: A140146 A140147 A140148 this_sequence A140150 A140151 
               A140152
%K A140149 nonn
%O A140149 1,2
%A A140149 Jasinski Artur (grafix(AT)csl.pl), May 12 2008

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