A051223 Number of ways of placing n nonattacking superqueens on an n X n board.

1, 0, 0, 0, 0, 0, 0, 0, 0, 4, 44, 156, 1876, 5180, 32516, 202900, 1330622, 8924976, 64492432, 495864256, 3977841852, 34092182276, 306819842212, 2883202816808, 28144109776812, 286022102245804

Offset

1,10

Comments

A superqueen moves like a queen and a knight.

A linear-time algorithm giving an explicit solution for any n >= 10 for the n-super-queens-problem can be found at the link. Included is an online solver, implemented in JavaScript. - Frank Schwellinger (nummer_eins(AT)web.de), Mar 19 2004. [But see the next comment - N. J. A. Sloane, Jul 01 2021]

Escamocher and O'Sullivan (2021) claim Schwellinger's algorithm is incorrect, and that their own algorithm is the first published linear-time algorithm. - N. J. A. Sloane, Jul 01 2021

Links

Table of n, a(n) for n=1..26.

D. Bill, Durango Bill's The N-Queens Problem

Guillaume Escamocher and Barry O'Sullivan, Leprechauns on the chessboard, Discrete Mathematics, 344(5), 2021. See especially page 3.

Vaclav Kotesovec, Non-attacking chess pieces, 6ed.

R. Oprisch, N x N SuperQueens Solutions Table

F. Schwellinger, Explicit Solution To the N-Super-Queens Problem.

W. Schubert, N-Queens page

Crossrefs

Cf. A051224, A000170.

Sequence in context: A292454 A292734 A053314 * A330651 A353542 A265081

Adjacent sequences: A051220 A051221 A051222 * A051224 A051225 A051226

Keyword

nonn,nice,more

Author

Ulrich Schimke (ulrschimke(AT)aol.com)

Extensions

a(20) from Bill link added Jul 25 2006

a(21)-a(23) from R. Oprisch's website added by Max Alekseyev, Sep 29 2006

a(24)-a(26) from W. Schubert, Jul 31 2009, Nov 29 2009, Jan 18 2011

Status

approved