A000901 Number of solutions to the rook problem on a 2n X 2n board having a certain symmetry group (see Robinson for details). (Formerly M4446 N1881)

0, 0, 7, 74, 882, 11144, 159652, 2571960, 46406392, 928734944, 20436096048, 490489794464, 12752891909920, 357081983435904, 10712466529388608, 342798976818878336, 11655165558112403328, 419585962575107694080, 15944266596501740800768, 637770663999955406424576, 26786367889087143196406272

Offset

1,3

References

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Amiram Eldar, Table of n, a(n) for n = 1..403

Loren C. Larson, The number of essentially different nonattacking rook arrangements, J. Recreat. Math., 7 (No. 3, 1974), circa pages 180-181. [Annotated scan of pages 180 and 181 only]

Édouard Lucas, Théorie des Nombres, Gauthier-Villars, Paris, 1891, Vol. 1, p. 222.

Édouard Lucas, Théorie des nombres (annotated scans of a few selected pages)

Robert W. Robinson, Counting arrangements of bishops, pp. 198-214 of Combinatorial Mathematics IV (Adelaide 1975), Lect. Notes Math., 560 (1976); Annotated scanned copy.

R. G. Wilson, v, Comments on the Larsen paper (no date).

Formula

a(n) ~ sqrt(2*Pi*n) * (2*n/e)^n / 4 (Robinson, 1976, p. 202). - Amiram Eldar, Jul 18 2026

Maple

# For Maple program see A000903.

Mathematica

a[n_] := (n!*2^n - If[OddQ[n], 0, n!/(n/2)!] - Sum[2^k*StirlingS1[n, k]*BellB[k], {k, 0, n}])/4; Array[a, 21] (* Amiram Eldar, Jul 18 2026 *)

Crossrefs

Cf. A000903.

Sequence in context: A275618 A377097 A114472 * A295245 A390385 A365844

Adjacent sequences: A000898 A000899 A000900 * A000902 A000903 A000904

Keyword

nonn,nice,changed

Author

N. J. A. Sloane and Robert G. Wilson v

Extensions

Corrected and extended by Sean A. Irvine, Aug 23 2011

More terms from Amiram Eldar, Jul 18 2026

Status

approved