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Search: id:A100097
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| A100097 |
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An inverse Chebyshev transform of the Pell numbers. |
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+0
3
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| 0, 1, 2, 8, 20, 64, 172, 512, 1416, 4096, 11468, 32768, 92248, 262144, 739832, 2097152, 5925520, 16777216, 47429900, 134217728, 379536440, 1073741824, 3036661032, 8589934592, 24294699120, 68719476736, 194363001272
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Image of x/(1-2x-x^2) under the transform g(x)->(1/sqrt(1-4x^2)g(xc(x^2)), where c(x) is the g.f. of the Catalan numbers A000108. This is the inverse of the Chebyshev transform which takes A(x) to ((1-x^2)/(1+x^2))A(x/(1+x^2)).
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FORMULA
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G.f.: x*sqrt(1-4x^2)(sqrt(1-4x^2)+2x)/((1-4x^2)(1-8x^2)); a(n)=sum{k=0..floor(n/2), binomial(n, k)*A000129(n-2k)}.
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CROSSREFS
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Cf. A100095, A100096.
Sequence in context: A024997 A081157 A099177 this_sequence A133467 A091004 A005559
Adjacent sequences: A100094 A100095 A100096 this_sequence A100098 A100099 A100100
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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 03 2004
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