A000900 Number of solutions to the rook problem on an n X n board having a certain symmetry group (see Robinson for details). (Formerly M1964 N0777)

0, 0, 0, 1, 2, 10, 28, 106, 344, 1272, 4592, 17692, 69384, 283560, 1191984, 5171512, 23087168, 105883456, 498572416, 2404766224, 11878871456, 59975885856, 309439708352, 1628919330208, 8746079933568, 47840206525056

Offset

0,5

References

L. C. Larson, The number of essentially different nonattacking rook arrangements, J. Recreat. Math., 7 (No. 3, 1974), circa pages 180-181.

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

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

T. D. Noe, Table of n, a(n) for n = 0..200

L. 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]

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

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

R. 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)=(A000085(n)-A000898(int(n/2)))/2

For asymptotics see the Robinson paper.

Maple

For Maple program see A000903.

Mathematica

a85[n_] := Sum[ (2k)!/k!/2^k Binomial[n, 2k], {k, 0, n/2}]; a898[n_] := Sum[ 2^k*StirlingS1[n, k]*BellB[k], {k, 0, n}]; a[n_] := (a85[n] - a898[Floor[n/2]])/2; a[1] = 0; Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Dec 13 2011, after formula *)

Crossrefs

Sequence in context: A296380 A291053 A104657 * A124023 A127921 A371943

Adjacent sequences: A000897 A000898 A000899 * A000901 A000902 A000903

Keyword

nonn,easy,nice

Author

N. J. A. Sloane

Extensions

More terms from Vladeta Jovovic, May 09 2000

Status

approved