A005631 Bishops on a 2n+1 X 2n+1 board (see Robinson paper for details). (Formerly M1628)

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

0,2

References

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=0..25.

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)

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 *)

Crossrefs

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

Cf. A005635.

Sequence in context: A358251 A002527 A005566 * A118677 A150043 A048117

Adjacent sequences: A005628 A005629 A005630 * A005632 A005633 A005634

Keyword

nonn

Author

N. J. A. Sloane

Extensions

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

Status

approved