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A267724 T(n,k)=Number of nXk arrays containing k copies of 0..n-1 with every element equal to at least one horizontal neighbor and the top left element equal to 0.

%I A267724 #6 Aug 12 2016 06:55:35
%S A267724 0,1,0,1,1,0,1,1,2,0,1,3,2,6,0,1,5,30,6,24,0,1,12,58,630,24,120,0,1,
%T A267724 26,588,1398,22680,120,720,0,1,60,2388,93672,55896,1247400,720,5040,0,
%U A267724 1,143,17456,609264,33807456,3353880,97297200,5040,40320,0,1,353,102874
%N A267724 T(n,k)=Number of nXk arrays containing k copies of 0..n-1 with every element equal to at least one horizontal neighbor and the top left element equal to 0.
%C A267724 Table starts
%C A267724 .0......1.....1...........1.........1...........1.........1........1.........1
%C A267724 .0......1.....1...........3.........5..........12........26.......60.......143
%C A267724 .0......2.....2..........30........58.........588......2388....17456....102874
%C A267724 .0......6.....6.........630......1398.......93672....609264.20702760.279681294
%C A267724 .0.....24....24.......22680.....55896....33807456.331295040
%C A267724 .0....120...120.....1247400...3353880.22933860480
%C A267724 .0....720...720....97297200.281725200
%C A267724 .0...5040..5040.10216206000
%C A267724 .0..40320.40320
%C A267724 .0.362880
%H A267724 R. H. Hardin, <a href="/A267724/b267724.txt">Table of n, a(n) for n = 1..70</a>
%e A267724 Some solutions for n=4 k=4
%e A267724 ..0..0..2..2....0..0..0..0....0..0..1..1....0..0..2..2....0..0..3..3
%e A267724 ..2..2..0..0....3..3..3..3....3..3..2..2....1..1..0..0....1..1..2..2
%e A267724 ..1..1..3..3....2..2..1..1....0..0..2..2....3..3..2..2....1..1..2..2
%e A267724 ..3..3..1..1....2..2..1..1....3..3..1..1....3..3..1..1....0..0..3..3
%Y A267724 Column 2 and column 3 are A000142(n-1).
%Y A267724 Column 4 is A007019(n-1).
%K A267724 nonn,tabl
%O A267724 1,9
%A A267724 _R. H. Hardin_, Jan 20 2016