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Search: id:A140145
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| A140145 |
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a(1)=1, a(n)=a(n-1)+n^1 if n odd, a(n)=a(n-1)+ n^3 if n is even. |
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+0
3
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| 1, 9, 12, 76, 81, 297, 304, 816, 825, 1825, 1836, 3564, 3577, 6321, 6336, 10432, 10449, 16281, 16300, 24300, 24321, 34969, 34992, 48816, 48841, 66417, 66444, 88396, 88425, 115425, 115456, 148224, 148257, 187561, 187596, 234252, 234289, 289161
(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+{[1+(-1)^n]/2}*n^3, with a(1)=1 a(n)=(3/16)-(1/4)*(-1)^n*n-(3/16)*(-1)^n+(1/4)*(-1)^n*n^3+(1/4)*n^3+(3/8)*(-1)^n*n^2+(3/8)*n^2+(1/4) *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-x^2+32*x^3-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 = 1; 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: A120991 A072308 A045769 this_sequence A166643 A038302 A050236
Adjacent sequences: A140142 A140143 A140144 this_sequence A140146 A140147 A140148
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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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