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A189791 Number of ways to place n nonattacking bishops on an 2n x 2n toroidal board. 3
4, 80, 2688, 132864, 8647680, 699678720, 67711795200, 7629571031040, 981168437329920, 141817953779712000, 22760391875493888000, 4016046336733347840000, 772743693378451931136000, 161027573368536472485888000, 36127883615009765477842944000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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)

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.

MATHEMATICA

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

CROSSREFS

Cf. A189790, A002465, A000172.

Sequence in context: A132584 A277074 A012127 * A057875 A187543 A268734

Adjacent sequences:  A189788 A189789 A189790 * A189792 A189793 A189794

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Apr 27 2011

STATUS

approved

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Last modified April 19 22:40 EDT 2021. Contains 343117 sequences. (Running on oeis4.)