A189791 Number of ways to place n nonattacking bishops on an 2n x 2n toroidal board.

4, 80, 2688, 132864, 8647680, 699678720, 67711795200, 7629571031040, 981168437329920, 141817953779712000, 22760391875493888000, 4016046336733347840000, 772743693378451931136000, 161027573368536472485888000, 36127883615009765477842944000

Offset: 1

Author

Vaclav Kotesovec, Apr 27 2011

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..200
• V. Kotesovec, Number of ways of placing non-attacking queens, kings, bishops and knights (in English and Czech)

Crossrefs

Cf. A189790, A002465, A000172.

Programs

Mathematica

Table[2^n*n!*Sum[Binomial[n,i]^3,{i,0,n}],{n,1,20}]

Formula

a(n)=2^n*n!*Sum[Binomial[n,i]^3,{i,0,n}].

Asymptotic: a(n) ~ 2^(4n+1)*(n-1)!/Pi/sqrt(3) ~ 2^(4n+1)*n^n/exp(n)*sqrt(2/(3*Pi*n)).

Recurrence: a(n) = ((14*n^2-14*n+4)*a(n-1) + 32*(n-1)^3*a(n-2))/n.