A109000 Antidiagonal sums of square array A108998, in which row n equals the coordination sequence of B_n lattice.

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

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