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T(n,k)=Number of nXk 0..1 arrays with no 1 equal to more than two of its horizontal and vertical neighbors, with the exception of exactly two elements.
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%I #4 Mar 03 2017 09:07:46

%S 0,0,0,0,0,0,0,1,1,0,0,6,34,6,0,0,49,395,395,49,0,0,272,3996,8592,

%T 3996,272,0,0,1376,37869,163860,163860,37869,1376,0,0,6620,338397,

%U 2875836,5814342,2875836,338397,6620,0,0,30552,2903399,47531178,188295479

%N T(n,k)=Number of nXk 0..1 arrays with no 1 equal to more than two of its horizontal and vertical neighbors, with the exception of exactly two elements.

%C Table starts

%C .0.....0........0...........0.............0................0..................0

%C .0.....0........1...........6............49..............272...............1376

%C .0.....1.......34.........395..........3996............37869.............338397

%C .0.....6......395........8592........163860..........2875836...........47531178

%C .0....49.....3996......163860.......5814342........188295479.........5735340380

%C .0...272....37869.....2875836.....188295479......11220964804.......628267302565

%C .0..1376...338397....47531178....5735340380.....628267302565.....64590243667344

%C .0..6620..2903399...753320466..167289795994...33653819417006...6347644826932771

%C .0.30552.24188526.11573758019.4724329890393.1744021436949798.603124906010664854

%H R. H. Hardin, <a href="/A283232/b283232.txt">Table of n, a(n) for n = 1..180</a>

%F Empirical for column k:

%F k=1: a(n) = a(n-1)

%F k=2: [order 15]

%F k=3: [order 27]

%F k=4: [order 51]

%e Some solutions for n=4 k=4

%e ..0..0..0..0. .1..1..0..1. .0..0..1..1. .0..0..1..1. .0..1..0..0

%e ..0..1..1..0. .1..0..1..1. .0..1..0..0. .0..1..1..0. .0..0..1..1

%e ..0..1..1..1. .1..1..1..0. .1..1..1..0. .1..1..1..0. .1..0..1..1

%e ..0..1..0..1. .1..1..0..0. .0..1..1..1. .0..1..0..1. .0..0..1..1

%K nonn,tabl

%O 1,12

%A _R. H. Hardin_, Mar 03 2017