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T(n,k)=Number of nXk arrays containing k copies of 0..n-1 with every element equal to at least one horizontal or antidiagonal neighbor and the top left element equal to 0.
5

%I #6 Aug 12 2016 06:55:35

%S 0,1,0,1,1,0,1,2,2,0,1,4,8,6,0,1,12,42,48,24,0,1,34,576,906,384,120,0,

%T 1,112,5492,59328,33120,3840,720,0,1,340,68958,2192682,10213152,

%U 1839720,46080,5040,0,1,1073,814418,131218206,1721696832,2641529760,144491760

%N T(n,k)=Number of nXk arrays containing k copies of 0..n-1 with every element equal to at least one horizontal or antidiagonal neighbor and the top left element equal to 0.

%C Table starts

%C .0.....1......1.........1..........1..........1.........1..........1.......1

%C .0.....1......2.........4.........12.........34.......112........340....1073

%C .0.....2......8........42........576.......5492.....68958.....814418.9982880

%C .0.....6.....48.......906......59328....2192682.131218206.6966218352

%C .0....24....384.....33120...10213152.1721696832

%C .0...120...3840...1839720.2641529760

%C .0...720..46080.144491760

%C .0..5040.645120

%C .0.40320

%C .0

%H R. H. Hardin, <a href="/A267617/b267617.txt">Table of n, a(n) for n = 1..59</a>

%e Some solutions for n=4 k=4

%e ..0..0..2..2....0..0..1..1....0..0..0..0....0..0..0..0....0..0..0..3

%e ..0..0..3..3....0..0..1..1....2..2..2..3....2..2..3..3....0..3..3..2

%e ..2..2..1..1....3..3..3..3....2..3..3..3....1..1..1..1....3..1..2..2

%e ..1..1..3..3....2..2..2..2....1..1..1..1....2..2..3..3....1..2..1..1

%Y Column 2 is A000142(n-1).

%Y Column 3 is A000165(n-1).

%K nonn,tabl

%O 1,8

%A _R. H. Hardin_, Jan 18 2016