A103330 Number of ways to place n+1 queens and a pawn on an n X n board so that no two queens attack each other.

0, 0, 0, 0, 0, 16, 20, 128, 396, 2288, 11152, 65712, 437848, 3118664, 23387448, 183463680, 1474699536, 12485203304, 110956890352, 1028589512656, 9801351322432, 97731300891440

Offset

1,6

Links

Table of n, a(n) for n=1..22.

Hans Bodlaender, The Nine Queens Problem, posted 4 January 2004.

R. D. Chatham, The N+k Queens Problem Page.

R. D. Chatham, The N+k Queens Problem Page.

R. D. Chatham, M. Doyle, G. H. Fricke, J. Reitmann, R. D. Skaggs and M. Wolff, Independence and Domination Separation in Chessboard Graphs, Journal of Combinatorial Mathematics and Combinatorial Computing 68 (2008).

R. D. Chatham, G. H. Fricke and R. D. Skaggs, The Queens Separation Problem, Utilitas Mathematica 69 (2006), 129-141.

Example

a(4) = 0 because when 5 queens are placed on a 4 X 4 board, at least 2 queens will be adjacent and therefore mutually attacking.

Crossrefs

Cf. A000170, A103331.

Sequence in context: A260572 A240038 A188242 * A045667 A045658 A167305

Adjacent sequences: A103327 A103328 A103329 * A103331 A103332 A103333

Keyword

more,nonn

Author

R. Douglas Chatham (d.chatham(AT)moreheadstate.edu), Jan 31 2005

Extensions

Further terms from R. Douglas Chatham (d.chatham(AT)moreheadstate.edu), Feb 15 2005, Apr 20 2007, Apr 28 2007

a(12) corrected by R. Douglas Chatham (d.chatham(AT)moreheadstate.edu), May 12 2009

a(18)-a(21) from Martin Ehrenstein, Oct 24 2023

a(22) from Martin Ehrenstein, Feb 09 2024

Status

approved