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

0,3

Links

Andrew Howroyd, Table of n, a(n) for n = 0..200

Vaclav Kotesovec, Non-attacking chess pieces, 6ed, 2013, p.422

Formula

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

Prog

(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

Crossrefs

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

Sequence in context: A155539 A285067 A234293 * A009480 A009481 A209498

Adjacent sequences: A244285 A244286 A244287 * A244289 A244290 A244291

Keyword

nonn

Author

Vaclav Kotesovec, Jun 25 2014

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

Status

approved