A197990 Number of binary arrangements of total n 1's, without adjacent 1's on n X n torus connected n-s.

1, 1, 4, 27, 664, 19375, 712536, 31474709, 1623421808, 95752130751, 6356272757680, 468976366239799, 38071162011854412, 3372179632719015287, 323631920261745650114, 33452466695808298399785, 3705187274710433648959456, 437779689881887196512539391

Offset: 0

Author

Vaclav Kotesovec, Oct 20 2011

Keywords

• nonn
• nice

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..200
• Vaclav Kotesovec, Non-attacking chess pieces, 6ed, 2013, p. 408.

Crossrefs

Cf. A067961, A197989.

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}]);
waz1t[k_,n_]:=(If[n-k+1Harvey P. Dale, Nov 24 2016 *)

PARI

a(n) = if(n<=1, 1, n*binomial(n^2-n-1,n-1) + n*(-1)^n) \\ Andrew Howroyd, Mar 27 2023

Formula

a(n) = n*binomial(n^2-n-1,n-1) + n*(-1)^n, n > 1. - Vaclav Kotesovec, Oct 20 2011

Extensions

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