

A018807


Number of ways to place n^2 nonattacking kings on 2n X 2n chessboard.


12



1, 4, 79, 3600, 281571, 32572756, 5109144543, 1027533353168, 254977173389319, 75925129079783308, 26568150968269086211, 10749154284380665611224, 4963704194366362387891227, 2588716234142991968960920692, 1511548995678989691821551648635
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OFFSET

0,2


COMMENTS

Rotations and reflections are considered distinct.
Also, number of ways to tile a (2n+1) X (2n+1) board with n^2 2 X 2 tiles and 4n+1 1 X 1 tiles, rotations and reflections counted as distinct.  David W. Wilson, Aug 18 2011
Number of maximum independent vertex sets in the 2n X 2n king graph.  Eric W. Weisstein, Jun 20 2017


LINKS

David W. Wilson, Table of n, a(n) for n = 0..26
Zealint Blog (Russian) Source for a(12) through a(20), March 14 2011. a(21) through a(26) from same source, July 9 2011.
V. Kotesovec, Nonattacking chess pieces, 6ed, 2013, pp. 160162.
Michael Larsen, The Problem of Kings, The Electronic Journal of Combinatorics 2, 1995
Eric Weisstein's World of Mathematics, King Graph
Eric Weisstein's World of Mathematics, Maximum Independent Vertex Set


FORMULA

Asymptotic (M. Larsen, 1995): log(a(n)) = 2n*log(n)  2n*log(2) + O(n^(4/5)*log(n)).


CROSSREFS

Cf. A174558, A174155, A174154, A173782, A173783, A061594, A061593.
Sequence in context: A048957 A006425 A065930 * A216410 A125710 A204296
Adjacent sequences: A018804 A018805 A018806 * A018808 A018809 A018810


KEYWORD

nonn,nice


AUTHOR

David W. Wilson


EXTENSIONS

a(0) added by Geoffrey H. Morley, Feb 06 2013


STATUS

approved



