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A217637 T(n,k)=Number of nXk arrays of the minimum value of corresponding elements and their horizontal and vertical neighbors in a random 0..1 nXk array.

%I A217637 #18 Jul 22 2025 23:41:45
%S A217637 2,2,2,4,6,4,6,16,16,6,10,38,66,38,10,16,98,244,244,98,16,26,244,968,
%T A217637 1418,968,244,26,42,614,3726,8706,8706,3726,614,42,68,1542,14520,
%U A217637 52120,83074,52120,14520,1542,68,110,3872,56352,315378,773348,773348,315378
%N A217637 T(n,k)=Number of nXk arrays of the minimum value of corresponding elements and their horizontal and vertical neighbors in a random 0..1 nXk array.
%C A217637 Number of maximal independent sets in the graph P_2 X P_n X P_k. - _Andrew Howroyd_, Jun 10 2017
%H A217637 R. H. Hardin, <a href="/A217637/b217637.txt">Table of n, a(n) for n = 1..220</a>
%H A217637 MacKenzie Carr, Christina M. Mynhardt, Ortrud R. Oellermann, <a href="https://arxiv.org/abs/2008.02781">Enumerating the Digitally Convex Sets of Powers of Cycles and Cartesian Products of Paths and Complete Graphs</a>, arXiv:2008.02781 [math.CO], 2020.
%H A217637 R. Euler, P. Oleksik, Z. Skupien, <a href="http://dx.doi.org/10.7151/dmgt.1707">Counting Maximal Distance-Independent Sets in Grid Graphs</a>, Discussiones Mathematicae Graph Theory. Volume 33, Issue 3, Pages 531-557, ISSN (Print) 2083-5892, July 2013; see <a href="http://www.degruyter.com/view/j/dmgt.2013.33.issue-3/dmgt.1707/dmgt.1707.xml">also</a>.
%e A217637 Table starts
%e A217637 ...2.....2........4..........6...........10..............16................26
%e A217637 ...2.....6.......16.........38...........98.............244...............614
%e A217637 ...4....16.......66........244..........968............3726.............14520
%e A217637 ...6....38......244.......1418.........8706...........52120............315378
%e A217637 ..10....98......968.......8706........83074..........773348...........7272142
%e A217637 ..16...244.....3726......52120.......773348........11181454.........163361868
%e A217637 ..26...614....14520.....315378......7272142.......163361868........3709621842
%e A217637 ..42..1542....56352....1900838.....68138974......2378097084.......83923710538
%e A217637 ..68..3872...218978...11472148....639248556.....34661572702.....1901055652804
%e A217637 .110..9726...850620...69210290...5994907930....505010822224....43046530809006
%e A217637 .178.24426..3304624..417586442..56226693158...7358779655656...974841850791586
%e A217637 .288.61348.12837742.2519466108.527340415924.107224919634686.22075731493018104
%e A217637 ...
%e A217637 Some solutions for n=3 k=4
%e A217637 ..1..0..0..1....0..0..0..1....1..0..1..1....1..1..0..0....1..0..0..0
%e A217637 ..0..0..0..0....0..0..1..1....0..0..0..1....0..0..1..0....1..1..0..0
%e A217637 ..1..0..0..0....0..0..0..1....1..0..1..1....0..0..0..1....1..0..0..0
%Y A217637 Columns 1-3 are A006355(n+1), A217631, A217632.
%Y A217637 Cf. A197054.
%K A217637 nonn,tabl
%O A217637 1,1
%A A217637 _R. H. Hardin_, Oct 09 2012