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

Author

Paul D. Hanna, Jun 17 2005

Keywords

• nonn

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.

Crossrefs

Cf. A108998, A108999, A109001.

Programs

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))))}

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)).