A005631 Bishops on a 2n+1 X 2n+1 board (see Robinson paper for details).

1, 2, 6, 18, 60, 200, 760, 2888, 11856, 48672, 215904, 957728, 4506304, 21203072, 105494400, 524880000, 2737670400, 14279148032, 77836363264, 424289980928, 2405307227136, 13635728197632, 80188215392256, 471566299547648, 2867649768509440, 17438513317683200

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

References

• 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). [The sequence psi(2k+1).]
• R. W. Robinson, Counting arrangements of bishops, pp. 198-214 of Combinatorial Mathematics IV (Adelaide 1975), Lect. Notes Math., 560 (1976). (Annotated scanned copy)

Crossrefs

Equals A123071(n)/2, n >= 1.

Cf. A005635.

Programs

Maple

For Maple program see A005635.

Mathematica

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]];
a[n_] := B[n + 1]*B[n + 2]/2;
Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Jul 23 2022, after Maple code for A123071 *)

Extensions

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