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T(n,k)=Number of nXk 0..1 arrays with no 1 equal to more than two of its horizontal, vertical and antidiagonal neighbors, with the exception of exactly one element.
7

%I #4 Mar 05 2017 10:24:13

%S 0,0,0,0,0,0,0,6,6,0,0,26,71,26,0,0,120,572,572,120,0,0,524,4398,7804,

%T 4398,524,0,0,2174,31952,106310,106310,31952,2174,0,0,8816,224927,

%U 1354928,2519010,1354928,224927,8816,0,0,35036,1546856,16714556,55886238

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

%C Table starts

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

%C .0.....0........6.........26..........120.............524..............2174

%C .0.....6.......71........572.........4398...........31952............224927

%C .0....26......572.......7804.......106310.........1354928..........16714556

%C .0...120.....4398.....106310......2519010........55886238........1199035122

%C .0...524....31952....1354928.....55886238......2154364298.......80410575348

%C .0..2174...224927...16714556...1199035122.....80410575348.....5221636463228

%C .0..8816..1546856..201420678..25121756412...2929763437610...330934422791290

%C .0.35036.10453311.2383832160.516765464924.104800502322828.20589913083547464

%H R. H. Hardin, <a href="/A283347/b283347.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 16]

%F k=3: [order 16]

%F k=4: [order 38]

%e Some solutions for n=4 k=4

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

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

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

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

%K nonn,tabl

%O 1,8

%A _R. H. Hardin_, Mar 05 2017