A005633 Bishops on an n X n board (see Robinson paper for details).

0, 1, 0, 2, 2, 8, 14, 36, 112, 216, 928, 1440, 8616, 11520, 87864, 100800, 997952, 1008000, 12427904, 10886400, 169435936, 130636800, 2501216992, 1676505600, 39837528576, 23471078400, 679494214656, 348713164800, 12370158205568, 5579410636800, 239109033342848

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

References

• R. W. Robinson, Counting arrangements of bishops, pp. 198-214 of Combinatorial Mathematics IV (Adelaide 1975), Lect. Notes Math., 560 (1976). [The sequence mu(n).]
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

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

For Maple program see A005635.

Mathematica

d[n_] := d[n] = If[n <= 1, 1, d[n - 1] + (n - 1)*d[n - 2]];
M[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]]]];
B[n_] := B[n] = Which[n == 0 || n == -2, 1, OddQ[n], B[n - 1], True, 2*B[n - 2] + (n - 2)*B[n - 4]];
S[n_] := S[n] = Module[{k}, If[Mod[n, 2]==0, 0, k = (n-1)/2; B[k]*B[k+1]]];
a[n_] := (M[n] - S[n])/2;
Table[a[n], {n, 1, 40}] (* Jean-François Alcover, Jul 23 2022, after Maple program in A005635 *)

Extensions

More terms from N. J. A. Sloane, Sep 28 2006