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%I #4 Mar 19 2013 16:35:17
%S 420,11610,357354,11206806,356391222,11391019146,365447949798,
%T 11741128578822,377630573527206,12150390210921654,391071237626540478,
%U 12588165595068116826,405241143066881319750,13045880634316557698334
%N 6X6X6 triangular graph coloring a rectangular array: number of nX3 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 3 of A223370
%H R. H. Hardin, <a href="/A223365/b223365.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 23*a(n-1) +897*a(n-2) -15543*a(n-3) -239874*a(n-4) +3284289*a(n-5) +27049393*a(n-6) -330039039*a(n-7) -1521495660*a(n-8) +18314438985*a(n-9) +47878976407*a(n-10) -618252955256*a(n-11) -889060713666*a(n-12) +13552173820568*a(n-13) +9580003346768*a(n-14) -201847740643953*a(n-15) -46867751747346*a(n-16) +2108268911742322*a(n-17) -184187510050618*a(n-18) -15779764589198623*a(n-19) +4879627711864385*a(n-20) +85835278187584234*a(n-21) -40138511702965646*a(n-22) -342053440022551516*a(n-23) +199639474840833405*a(n-24) +1001161151524243334*a(n-25) -671464975697570928*a(n-26) -2146406246471550814*a(n-27) +1582756069996035189*a(n-28) +3342452561011804599*a(n-29) -2639262830436925013*a(n-30) -3723873632097428362*a(n-31) +3096692775113977724*a(n-32) +2897671400594634762*a(n-33) -2511627603739201088*a(n-34) -1516552491534508238*a(n-35) +1362811032192743844*a(n-36) +502215369425262432*a(n-37) -467555871709031156*a(n-38) -94719302460861132*a(n-39) +91628605259689448*a(n-40) +8417956616498704*a(n-41) -8338690645967040*a(n-42) -301027284753856*a(n-43) +203944076489856*a(n-44) +12153311182848*a(n-45) +24038117888*a(n-46)
%e Some solutions for n=3
%e .12..8.13....2..1..2....4..7.12....4..7.12....4..7.11....4..8..9....4..3..4
%e ..8.12..8....5..4..1....3..4..8....3..4..8....1..4..7....8..4..5....7..4..5
%e .12.11.12....8..5..2....4..8.13....4..3..4....2..1..3....7..8..4....4..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
%O 1,1
%A _R. H. Hardin_ Mar 19 2013
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