%I A002562 M0180 N0068
%S A002562 1,0,0,1,2,1,6,12,46,92,341,1787,9233,45752,285053,1846955,11977939,
%T A002562 83263591,621012754,4878666808,39333324973,336376244042,3029242658210,
%U A002562 28439272956934,275986683743434,2789712466510289
%N A002562 Number of ways of placing n nonattacking queens on n X n board (symmetric 
               solutions count only once).
%D A002562 J. R. Bitner and E. M. Reingold, Backtrack programming techniques, Commun. 
               ACM, 18 (1975), 651-656.
%D A002562 M. A. Sainte-Lagu\"{e}, Les R\'{e}seaux (ou Graphes)}, M\'{e}morial des 
               Sciences Math\'{e}matiques, Fasc. 18, Gauthier-Villars, Paris, 1926, 
               p. 47.
%D A002562 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A002562 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A002562 M. B. Wells, Elements of Combinatorial Computing. Pergamon, Oxford, 1971, 
               p. 238.
%H A002562 Thomas Preusser, <a href="http://queens.inf.tu-dresden.de">Queens%40TUD</
               a>-Project
%H A002562 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               QueensProblem.html">Link to a section of The World of Mathematics.</
               a>
%F A002562 a(n) = 1/8 * (Q(n) + P(n) + 2 * R(n)), where Q(n) = A000170(n) [all solutions], 
               P(n) = A032522(n) [point symmetric solutions] and R(n) = A033148(n) 
               [rotationally symmetric solutions].
%Y A002562 Cf. A000170, A032522, A033148.
%Y A002562 Sequence in context: A113216 A081064 A128534 this_sequence A136456 A123968 
               A068797
%Y A002562 Adjacent sequences: A002559 A002560 A002561 this_sequence A002563 A002564 
               A002565
%K A002562 nonn,nice
%O A002562 1,5
%A A002562 N. J. A. Sloane (njas(AT)research.att.com).
%E A002562 a(17) and a(18) found by Ulrich Schimke in Goettingen, Germany (UlrSchimke(AT)aol.com)
%E A002562 Formula and a(19) to a(23) added by Matthias Engelhardt in Nuernberg, 
               Germany, 2000-01-23 (Matthias.R.Engelhardt(AT)web.de)
%E A002562 Added terms calculated from formula. Thomas B. Preusser (thomas.preusser(AT)tu-dresden.de), 
               Dec 15 2008
%E A002562 Added a(26) derived by formula after recent extension of A000170. Thomas 
               B. Preusser (thomas.preusser(AT)tu-dresden.de), Jul 12 2009