A005633 Bishops on an n X n board (see Robinson paper for details). (Formerly M0376)

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

1,4

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

Table of n, a(n) for n=1..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

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 *)

Crossrefs

Sequence in context: A045686 A045677 A280399 * A228661 A369316 A026585

Adjacent sequences: A005630 A005631 A005632 * A005634 A005635 A005636

Keyword

nonn

Author

N. J. A. Sloane.

Extensions

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

Status

approved