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%I #4 Mar 19 2013 16:38:44
%S 21,90,90,420,990,420,1992,11610,11610,1992,9552,139158,357354,139158,
%T 9552,45984,1686042,11206806,11206806,1686042,45984,221760,20537766,
%U 356391222,933306108,356391222,20537766,221760,1070208,250834914
%N T(n,k)=6X6X6 triangular graph coloring a rectangular array: number of nXk 0..20 arrays where 0..20 label nodes of the fully triangulated graph and every array movement to a horizontal or vertical neighbor moves along an edge of this graph
%C Table starts
%C .......21...........90...............420..................1992
%C .......90..........990.............11610................139158
%C ......420........11610............357354..............11206806
%C .....1992.......139158..........11206806.............933306108
%C .....9552......1686042.........356391222...........78876317946
%C ....45984.....20537766.......11391019146.........6710970374274
%C ...221760....250834914......365447949798.......573055927043172
%C ..1070208...3067525350....11741128578822.....49029858427514634
%C ..5166336..37537522362...377630573527206...4199534828773389870
%C .24943104.459492912054.12150390210921654.359921587558219055304
%H R. H. Hardin, <a href="/A223370/b223370.txt">Table of n, a(n) for n = 1..112</a>
%e Some solutions for n=3 k=4
%e ..0..2..0..2....1..2..0..1....0..1..4..3....0..1..3..1....0..2..0..2
%e ..2..0..2..4....2..5..2..0....1..4..1..4....1..2..4..2....2..4..2..4
%e ..5..2..4..2....1..2..5..2....3..1..3..7....4..5..2..1....1..2..1..2
%e Vertex neighbors:
%e 0 -> 1 2
%e 1 -> 0 2 3 4
%e 2 -> 0 1 4 5
%e 3 -> 1 4 6 7
%e 4 -> 1 2 3 5 7 8
%e 5 -> 2 4 8 9
%e 6 -> 3 7 10 11
%e 7 -> 3 4 6 8 11 12
%e 8 -> 4 5 7 9 12 13
%e 9 -> 5 8 13 14
%e 10 -> 6 11 15 16
%e 11 -> 6 7 10 12 16 17
%e 12 -> 7 8 11 13 17 18
%e 13 -> 8 9 12 14 18 19
%e 14 -> 9 13 19 20
%e 15 -> 10 16
%e 16 -> 10 11 15 17
%e 17 -> 11 12 16 18
%e 18 -> 12 13 17 19
%e 19 -> 13 14 18 20
%e 20 -> 14 19
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_ Mar 19 2013
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