A244288 Number of binary arrangements of total n 1's, without adjacent 1's on n X n array connected nw-se.

1, 1, 5, 57, 1084, 29003, 999717, 42125233, 2096106904, 120194547233, 7799803041491, 564856080384900, 45146219773912540, 3946445378386791157, 374482268128153003615, 38330653031858936914329, 4209191997519328986666624, 493575737047609363968826907

Offset: 0

Author

Vaclav Kotesovec, Jun 25 2014

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..200
• Vaclav Kotesovec, Non-attacking chess pieces, 6ed, 2013, p.422

Crossrefs

Cf. A197989, A201540, A201511, A201861, A201513, A244284.

Programs

PARI

P(m,n) = sum(k=0, (m+1)\2, binomial(m-k+1,k)*x^k, O(x*x^n))
a(n) = polcoef(P(n,n)*prod(m=1, n-1, P(m,n))^2, n) \\ Andrew Howroyd, Mar 27 2023

Formula

a(n) ~ n^(2*n)/n! * exp(-3/2).

Extensions

a(16) from Vaclav Kotesovec, Sep 04 2016

a(17) from Vaclav Kotesovec, Jun 15 2021

a(0)=1 prepended by Andrew Howroyd, Mar 27 2023