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

Author

David W. Wilson

Keywords

• nonn
• nice

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

Crossrefs

Main diagonal of A350819.

Cf. A174558, A174155, A174154, A173782, A173783, A061594, A061593.

Formula

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

Extensions

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