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Search: id:A109000
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| A109000 |
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Antidiagonal sums of square array A108998, in which row n equals the coordination sequence of B_n lattice. |
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4
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| 1, 1, 3, 11, 37, 133, 479, 1719, 6121, 21609, 75675, 263171, 909899, 3130963, 10730891, 36639987, 124528283, 420319907, 1403656123, 4615627555, 14868713515, 46702912307, 142489152555, 421113970835, 1203581558011
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Limit a(n+1)/a(n) ~ 3.3829757679..., real root of cubic (1+x+3*x^2-x^3). Compare to antidiagonal sums A108555 of square array A108553, in which row n equals the crystal ball sequence for D_n lattice.
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FORMULA
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a(n) = Sum_{k=0..n} Sum_{j=0..k} C(n-j-1, k-j) * (C(2*n-2*k+1, 2*j)-2*(n-k)*C(n-k-1, j-1)).
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PROGRAM
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(PARI) {a(n)=sum(k=0, n, sum(j=0, k, binomial(n-j-1, k-j)*(binomial(2*n-2*k+1, 2*j)-2*(n-k)*binomial(n-k-1, j-1))))}
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CROSSREFS
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Cf. A108998, A108999, A109001.
Adjacent sequences: A108997 A108998 A108999 this_sequence A109001 A109002 A109003
Sequence in context: A027066 A046722 A047102 this_sequence A129962 A026361 A006189
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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), Jun 17 2005
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