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A109000 Antidiagonal sums of square array A108998, in which row n equals the coordination sequence of B_n lattice. 3
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; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

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.

LINKS

Table of n, a(n) for n=0..24.

FORMULA

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)).

PROG

(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))))}

CROSSREFS

Cf. A108998, A108999, A109001.

Sequence in context: A180168 A232031 A047102 * A183511 A307800 A265796

Adjacent sequences:  A108997 A108998 A108999 * A109001 A109002 A109003

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jun 17 2005

STATUS

approved

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Last modified May 28 12:18 EDT 2020. Contains 334681 sequences. (Running on oeis4.)