A244288 - OEIS

%I #14 Mar 27 2023 22:37:07

%S 1,1,5,57,1084,29003,999717,42125233,2096106904,120194547233,

%T 7799803041491,564856080384900,45146219773912540,3946445378386791157,

%U 374482268128153003615,38330653031858936914329,4209191997519328986666624,493575737047609363968826907

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

%H Andrew Howroyd, <a href="/A244288/b244288.txt">Table of n, a(n) for n = 0..200</a>

%H Vaclav Kotesovec, <a href="https://oeis.org/wiki/User:Vaclav_Kotesovec">Non-attacking chess pieces</a>, 6ed, 2013, p.422

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

%o (PARI) P(m,n) = sum(k=0, (m+1)\2, binomial(m-k+1,k)*x^k, O(x*x^n))

%o a(n) = polcoef(P(n,n)*prod(m=1, n-1, P(m,n))^2, n) \\ _Andrew Howroyd_, Mar 27 2023

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

%K nonn

%O 0,3

%A _Vaclav Kotesovec_, Jun 25 2014

%E a(16) from _Vaclav Kotesovec_, Sep 04 2016

%E a(17) from _Vaclav Kotesovec_, Jun 15 2021

%E a(0)=1 prepended by _Andrew Howroyd_, Mar 27 2023