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Search: id:A113954
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| A113954 |
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Expansion of (1-2x^2)/((1-2x)(1+x)^2). |
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+0
3
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| 1, 0, 1, 2, 3, 8, 13, 30, 55, 116, 225, 458, 907, 1824, 3637, 7286, 14559, 29132, 58249, 116514, 233011, 466040, 932061, 1864142, 3728263, 7456548, 14913073, 29826170, 59652315, 119304656, 238609285, 477218598, 954437167, 1908874364, 3817748697
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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Inverse binomial transform of phi(phi(3^n)).
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FORMULA
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a(n)=3a(n-2)+2a(n-3); a(n)=2^(n+1)/9+(7-3n)(-1)^n/9; a(n)=a(n)=sum{k=0..n, (-1)^(n-k)*C(n, k)phi(phi(3^k))}; a(n)=sum{k=0..n, (-1)^(n-k)*C(n, k)(2*3^k/9+C(1, k)/3+4*C(0, k)/9)}; a(n)=sum{k=0..n, J(n-k+1)((-1)^(k+1)-2C(1, k)+4C(0, k))} where J(n)=A001045(n).
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CROSSREFS
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Cf. A103196.
Sequence in context: A105204 A045692 A103196 this_sequence A025082 A129873 A025575
Adjacent sequences: A113951 A113952 A113953 this_sequence A113955 A113956 A113957
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Nov 09 2005
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