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%I #4 Mar 18 2013 17:46:56
%S 624,48114,4232586,367156350,32213930742,2819203560630,
%T 247143798101322,21653415762483246,1897735773641654046,
%U 166300121937966179310,14573870195990661027330,1277163080979499793030130
%N 3X3X3 triangular graph coloring a rectangular array: number of nX5 0..5 arrays where 0..5 label nodes of a graph with edges 0,1 0,2 1,2 1,3 1,4 2,4 3,4 2,5 4,5 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph
%C Column 5 of A223218
%H R. H. Hardin, <a href="/A223215/b223215.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 64*a(n-1) +3496*a(n-2) -104128*a(n-3) -2437410*a(n-4) +49302884*a(n-5) +557525760*a(n-6) -9465346688*a(n-7) -53592872633*a(n-8) +868267508240*a(n-9) +2235257041399*a(n-10) -41069041856528*a(n-11) -36491801604768*a(n-12) +1061861955280348*a(n-13) -32518628901806*a(n-14) -15720782954090080*a(n-15) +8280943406836616*a(n-16) +139041174144887408*a(n-17) -112580871139611713*a(n-18) -753441986044479920*a(n-19) +742544685340720320*a(n-20) +2520998438780302208*a(n-21) -2793597033221247360*a(n-22) -5173462381751115264*a(n-23) +6291736944543350272*a(n-24) +6359191157618116608*a(n-25) -8671729791397443584*a(n-26) -4363943425625771008*a(n-27) +7344832317209315328*a(n-28) +1297000451641442304*a(n-29) -3753223506173448192*a(n-30) +157481325008027648*a(n-31) +1106554234568310784*a(n-32) -219305825967177728*a(n-33) -171321792926318592*a(n-34) +57655910201294848*a(n-35) +10784605931569152*a(n-36) -6327661169213440*a(n-37) +107512997085184*a(n-38) +282873139560448*a(n-39) -33534391615488*a(n-40) -3153512628224*a(n-41) +696053137408*a(n-42) -10200547328*a(n-43) -3221225472*a(n-44) +134217728*a(n-45)
%e Some solutions for n=3
%e ..0..1..3..1..3....0..2..0..1..2....0..1..0..1..2....0..2..4..5..4
%e ..1..0..1..4..1....1..4..1..2..5....1..0..2..4..5....1..4..2..4..2
%e ..0..2..4..5..2....0..1..4..1..4....0..1..4..5..4....0..2..4..2..4
%K nonn
%O 1,1
%A _R. H. Hardin_ Mar 18 2013
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