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

Author

N. J. A. Sloane, Sep 25 2006

Keywords

• nonn

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

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

Programs

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 *)