A018807 Number of ways to place n^2 nonattacking kings on 2n X 2n chessboard.

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

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.

Tricia Muldoon Brown, Queens, Attack!, The Mathematical Intelligencer (2020).

Tricia Muldoon Brown, Maximum arrangements of nonattacking kings on the 2n × 2n chessboard, Georgia Southern University (2020).

Vaclav Kotesovec, Non-attacking chess pieces, 6ed, 2013, pp. 160-162.

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

Main diagonal of A350819.

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