A122748 Bishops on an n X n board (see Robinson paper for details).

1, 1, 2, 2, 4, 8, 16, 40, 72, 260, 432, 1976, 2880, 17632, 23040, 177248, 201600, 2001680, 2016000, 24879520, 21772800, 338969216, 261273600, 5002865792, 3353011200, 79676972608, 46942156800, 1358997441920, 697426329600, 24740358817280, 11158821273600, 478218277674496

Offset

0,3

References

R. W. Robinson, Counting arrangements of bishops, pp. 198-214 of Combinatorial Mathematics IV (Adelaide 1975), Lect. Notes Math., 560 (1976). (M_n, p. 208)

Links

Table of n, a(n) for n=0..31.

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

unprotect(D); D:=proc(n) option remember; if n <= 1 then 1 else D(n-1)+(n-1)*D(n-2); fi; end; # Gives A000085
M:=proc(n) local k; if n mod 2 = 0 then k:=n/2; if k mod 2 = 0 then RETURN( k!*(k+2)/2 ); else RETURN( (k-1)!*(k+1)^2/2 ); fi; else k:=(n-1)/2; RETURN(D(k)*D(k+1)); fi; end;

Mathematica

d[n_] := d[n] = If[n <= 1, 1, d[n - 1] + (n - 1)*d[n - 2]];
a[n_] := Module[{k}, If[Mod[n, 2] == 0, k = n/2; If[Mod[k, 2] == 0, Return[k!*(k + 2)/2], Return[(k - 1)!*(k + 1)^2/2]], k = (n - 1)/2; Return[d[k]*d[k + 1]]]];
Table[a[n], {n, 0, 40}] (* Jean-François Alcover, Jul 23 2022, after Maple code *)

Crossrefs

Sequence in context: A090129 A001137 A123593 * A108774 A063402 A175195

Adjacent sequences: A122745 A122746 A122747 * A122749 A122750 A122751

Keyword

nonn

Author

N. J. A. Sloane, Sep 25 2006

Status

approved