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Search: id:A140149
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| A140149 |
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a(1)=1, a(n)=a(n-1)+n^2 if n odd, a(n)=a(n-1)+ n^3 if n is even. |
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+0
2
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| 1, 9, 18, 82, 107, 323, 372, 884, 965, 1965, 2086, 3814, 3983, 6727, 6952, 11048, 11337, 17169, 17530, 25530, 25971, 36619, 37148, 50972, 51597, 69173, 69902, 91854, 92695, 119695, 120656, 153424, 154513, 193817, 195042, 241698, 243067
(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^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
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]
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MATHEMATICA
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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*)
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CROSSREFS
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Cf. A000027, A000217, A000330, A000537, A000538, A000539, A136047, A140113.
Sequence in context: A022669 A107313 A166640 this_sequence A066711 A033651 A050250
Adjacent sequences: A140146 A140147 A140148 this_sequence A140150 A140151 A140152
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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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