cp's OEIS Frontend

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.

%I A103330 #29 Aug 10 2025 19:12:15
%S A103330 0,0,0,0,0,16,20,128,396,2288,11152,65712,437848,3118664,23387448,
%T A103330 183463680,1474699536,12485203304,110956890352,1028589512656,
%U A103330 9801351322432,97731300891440,1014610719838792
%N 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.
%H A103330 Hans Bodlaender, <a href="https://www.chessvariants.com/problems.dir/9queens.html">The Nine Queens Problem</a>, posted 4 January 2004.
%H A103330 R. D. Chatham, <a href="https://web.archive.org/web/20120717025715/http://people.moreheadstate.edu/fs/d.chatham/nkqueens.html">The N+k Queens Problem Page</a>.
%H A103330 R. D. Chatham, <a href="http://www.npluskqueens.info/">The N+k Queens Problem Page</a>.
%H A103330 R. D. Chatham, M. Doyle, G. H. Fricke, J. Reitmann, R. D. Skaggs and M. Wolff, <a href="https://www.researchgate.net/publication/228970881_Independence_and_domination_separation_on_chessboard_graphs">Independence and Domination Separation in Chessboard Graphs</a>, Journal of Combinatorial Mathematics and Combinatorial Computing 68 (2008).
%H A103330 R. D. Chatham, G. H. Fricke and R. D. Skaggs, <a href="https://www.researchgate.net/publication/264996366_The_Queens_separation_problem">The Queens Separation Problem</a>, Utilitas Mathematica 69 (2006), 129-141.
%e A103330 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.
%Y A103330 Cf. A000170, A103331.
%K A103330 more,nonn
%O A103330 1,6
%A A103330 R. Douglas Chatham (d.chatham(AT)moreheadstate.edu), Jan 31 2005
%E A103330 Further terms from R. Douglas Chatham (d.chatham(AT)moreheadstate.edu), Feb 15 2005, Apr 20 2007, Apr 28 2007
%E A103330 a(12) corrected by R. Douglas Chatham (d.chatham(AT)moreheadstate.edu), May 12 2009
%E A103330 a(18)-a(21) from _Martin Ehrenstein_, Oct 24 2023
%E A103330 a(22) from _Martin Ehrenstein_, Feb 09 2024
%E A103330 a(23) computed on a GPU using CUDA by _Martin Ehrenstein_, Aug 10 2025