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
Keywords
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
- 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
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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;
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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 *)