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A223364 6X6X6 triangular graph coloring a rectangular array: number of nX2 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 1

%I

%S 90,990,11610,139158,1686042,20537766,250834914,3067525350,

%T 37537522362,459492912054,5625465499458,68876427444102,

%U 843332143519674,10326055803410934,126436970898858978,1548158980998752262

%N 6X6X6 triangular graph coloring a rectangular array: number of nX2 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 2 of A223370

%H R. H. Hardin, <a href="/A223364/b223364.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 17*a(n-1) -44*a(n-2) -208*a(n-3) +363*a(n-4) +659*a(n-5) -448*a(n-6) -364*a(n-7) +66*a(n-8) +24*a(n-9)

%e Some solutions for n=3

%e ..4..7....7.11...11..6...11.17...13.12....8.13....0..1....6..3....8.13....8.12

%e ..2..4...12..7...12.11...17.12...12.17....4..8....2..4...11..7....9.14....4..8

%e ..4..2...11.12...11..6...11..7...13.18....5..4....1..3....6..3....8.13....8..7

%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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Last modified May 24 10:26 EDT 2022. Contains 354027 sequences. (Running on oeis4.)