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Search: id:A092566
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| A092566 |
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Main diagonal of triangle A092565, in which the n-th row polynomial equals the numerator of the n-th convergent of the continued fraction [1+x+x^2;1+x+x^2,1+x+x^2,...]. |
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+0
2
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| 1, 1, 3, 7, 22, 63, 191, 573, 1752, 5372, 16597, 51465, 160258, 500551, 1567881, 4922687, 15488481, 48821964, 154147654, 487412324, 1543231353, 4891986889, 15524303265, 49314008259, 156791992914, 498931763064, 1588891019625
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OFFSET
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0,3
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FORMULA
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a(n) = sum_{k=0..n} A037027(n, k)*C(k, n-k).
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PROGRAM
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(PARI) a(n)=if(n<0, 0, polcoeff(contfracpnqn(vector(n, i, 1+x+x^2))[1, 1], n, x)) (PARI) A037027(n, k)=if(n<k|k<0, 0, sum(j=0, n-k, binomial(j+k, k)*binomial(j, n- j-k))) a(n)=sum(k=0, n, A037027(n, k)*binomial(k, n-k))
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CROSSREFS
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Cf. A092565, A037027.
Sequence in context: A128599 A080882 A079120 this_sequence A036719 A166135 A007595
Adjacent sequences: A092563 A092564 A092565 this_sequence A092567 A092568 A092569
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Feb 28 2004
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