A122693 Bishops on an n X n board (see Robinson paper for details).

0, 2, 4, 32, 128, 1152, 6912, 73728, 589824, 7372800, 73728000, 1061683200, 12740198400, 208089907200, 2913258700800, 53271016243200, 852336259891200, 17259809262796800, 310676566730342400, 6903923705118720000, 138078474102374400000, 3341499073277460480000

Offset

0,2

References

R. W. Robinson, Counting arrangements of bishops, pp. 198-214 of Combinatorial Mathematics IV (Adelaide 1975), Lect. Notes Math., 560 (1976). (C_{2n+1}, Eq. (20))

Links

Table of n, a(n) for n=0..21.

R. W. Robinson, Counting arrangements of bishops, pp. 198-214 of Combinatorial Mathematics IV (Adelaide 1975), Lect. Notes Math., 560 (1976). (Annotated scanned copy)

Maple

C:=proc(n) local k; if n mod 2 = 0 then RETURN(0); fi; k:=(n-1)/2; if k mod 2 = 0 then RETURN( k*2^(k-1)*((k/2)!)^2 ); else RETURN( 2^k*(((k+1)/2)!)^2 ); fi; end; [seq(C(2*n+1), n=0..30)];

Mathematica

c[n_] := Module[{k}, If[Mod[n, 2] == 0, 0, k = (n-1)/2; If[Mod[k, 2] == 0, k*2^(k-1)*((k/2)!)^2, 2^k*(((k+1)/2)!)^2]]];
a[n_] := c[2n+1];
Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Jul 23 2022, after Maple code *)

Crossrefs

Sequence in context: A192387 A320624 A133127 * A019060 A366365 A247014

Adjacent sequences: A122690 A122691 A122692 * A122694 A122695 A122696

Keyword

nonn

Author

N. J. A. Sloane, Sep 25 2006

Status

approved