%I #4 Mar 20 2013 05:45:22
%S 120,1648,25436,394736,6256832,98783592,1575629948,24993296408,
%T 399339124688,6343618034616,101407143454528,1611628793976896,
%U 25766710390525620,409564700700266752,6548402342102019564
%N 5X5X5 triangular graph without horizontal edges coloring a rectangular array: number of nX3 0..14 arrays where 0..14 label nodes of a graph with edges 0,1 0,2 1,3 1,4 2,4 2,5 3,6 3,7 4,7 4,8 5,8 5,9 6,10 6,11 7,11 7,12 8,12 8,13 9,13 9,14 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph
%C Column 3 of A223432
%H R. H. Hardin, <a href="/A223427/b223427.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 466*a(n-2) -69185*a(n-4) +4382193*a(n-6) -130562793*a(n-8) +2110263466*a(n-10) -20078358067*a(n-12) +116999028688*a(n-14) -423034699529*a(n-16) +947474341907*a(n-18) -1308325237689*a(n-20) +1105531342712*a(n-22) -563527872936*a(n-24) +167881696044*a(n-26) -27388441192*a(n-28) +2145049440*a(n-30) -57784320*a(n-32) for n>33
%e Some solutions for n=3
%e ..7..3..1....4..7..3....1..4..7....6.11..7....3..6..3...11..7..4....4..7.11
%e ..3..7..4....1..3..1....4..7.12....3..6.11....7.11..6....7..4..2....7.11..7
%e ..1..4..8....0..1..0....8.12..7....6.11..6...11..6.10...12..8..5...12..7.11
%K nonn
%O 1,1
%A _R. H. Hardin_ Mar 20 2013