A018807 - OEIS

%I #71 Mar 27 2023 22:36:55

%S 1,4,79,3600,281571,32572756,5109144543,1027533353168,254977173389319,

%T 75925129079783308,26568150968269086211,10749154284380665611224,

%U 4963704194366362387891227,2588716234142991968960920692,1511548995678989691821551648635

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

%C Rotations and reflections are considered distinct.

%C 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

%C Number of maximum independent vertex sets in the 2n X 2n king graph. - _Eric W. Weisstein_, Jun 20 2017

%H David W. Wilson, <a href="/A018807/b018807.txt">Table of n, a(n) for n = 0..26</a>

%H Zealint Blog (Russian) <a href="http://zealint.ru/maxflow-kings-1dwalks-comp.html">Source for a(12) through a(20)</a>, March 14 2011. a(21) through a(26) from same source, July 9 2011.

%H Tricia Muldoon Brown, <a href="https://doi.org/10.1007/s00283-019-09963-y">Queens, Attack!</a>, The Mathematical Intelligencer (2020).

%H Tricia Muldoon Brown, <a href="https://www.researchgate.net/publication/345816618_MAXIMUM_ARRANGEMENTS_OF_NONATTACKING_KINGS_ON_THE_2n_2n_CHESSBOARD">Maximum arrangements of nonattacking kings on the 2n &times; 2n chessboard</a>, Georgia Southern University (2020).

%H Vaclav Kotesovec, <a href="https://oeis.org/wiki/User:Vaclav_Kotesovec">Non-attacking chess pieces</a>, 6ed, 2013, pp. 160-162.

%H Michael Larsen, <a href="http://www.combinatorics.org/Volume_2/Abstracts/v2i1r18.html">The Problem of Kings</a>, The Electronic Journal of Combinatorics 2, 1995

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/KingGraph.html">King Graph</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MaximumIndependentVertexSet.html">Maximum Independent Vertex Set</a>

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

%Y Main diagonal of A350819.

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

%K nonn,nice

%O 0,2

%A _David W. Wilson_

%E a(0) added by _Geoffrey H. Morley_, Feb 06 2013