A197989 Number of binary arrangements of total n 1's, without adjacent 1's on n X n array connected n-s.

1, 4, 45, 886, 24395, 860336, 36914493, 1863645610, 108131503623, 7085585223652, 517329551346608, 41634263983867842, 3661077644199252550, 349191617521920855488, 35902782820742394839453, 3958207187579046500083794, 465777357329812920074875295

Offset: 1

Author

Vaclav Kotesovec, Oct 20 2011

Keywords

• nonn
• nice
• hard

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 1..108
• V. Kotesovec, Non-attacking chess pieces, 6ed, p.373-381

Crossrefs

Cf. A067966, A197990.

Programs

Mathematica

permopak[part_,k_]:=(hist=ConstantArray[0,k];
Do[hist[[part[[t]]]]++,{t,1,Length[part]}];
(Length[part])!/Product[(hist[[t]])!,{t,1,k}]);
waz1n[k_,n_]:=(If[n-k+1
				

Formula

Asymptotic (V. Kotesovec, Oct 15 2011): a(n) ~ n^(2n)/n!*exp(-3/2).