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%I #4 Mar 19 2013 16:37:59
%S 221760,250834914,365447949798,573055927043172,928457167048336590,
%T 1524391185435213940170,2520297393549555690831036,
%U 4179551352031701135658304214,6944490071035753511344864688838
%N 6X6X6 triangular graph coloring a rectangular array: number of nX7 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 Column 7 of A223370
%H R. H. Hardin, <a href="/A223369/b223369.txt">Table of n, a(n) for n = 1..71</a>
%e Some solutions for n=3
%e ..0..1..0..1..3..6..3....0..1..0..2..5..2..0....0..1..0..2..5..2..5
%e ..1..0..2..0..1..3..1....1..0..2..4..2..4..1....1..0..2..0..2..0..2
%e ..0..2..0..1..4..7..4....0..2..0..2..5..8..4....0..2..0..1..0..2..4
%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
%O 1,1
%A _R. H. Hardin_ Mar 19 2013
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