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Search: id:A140154
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| A140154 |
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a(1)=1, a(n)=a(n-1)+n^3 if n odd, a(n)=a(n-1)+ n^2 if n is even. |
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+0
2
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| 1, 5, 32, 48, 173, 209, 552, 616, 1345, 1445, 2776, 2920, 5117, 5313, 8688, 8944, 13857, 14181, 21040, 21440, 30701, 31185, 43352, 43928, 59553, 60229, 79912, 80696, 105085, 105985, 135776, 136800, 172737, 173893, 216768, 218064, 268717
(list; graph; listen)
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OFFSET
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1,2
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FORMULA
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a(n)=a(n-1)+{[1-(-1)^n]/2}*n^3+{[1+(-1)^n]/2}*n^2, 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
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*(x^2+1)*(x^4-4*x^3+22*x^2+4*x+1)/((1+x)^4*(x-1)^5). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 22 2009]
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MATHEMATICA
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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*)
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CROSSREFS
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Cf. A000027, A000217, A000330, A000537, A000538, A000539, A136047, A140113.
Sequence in context: A062631 A156027 A100840 this_sequence A073694 A101966 A089574
Adjacent sequences: A140151 A140152 A140153 this_sequence A140155 A140156 A140157
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KEYWORD
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nonn
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AUTHOR
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Jasinski Artur (grafix(AT)csl.pl), May 12 2008
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