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A223213 3X3X3 triangular graph coloring a rectangular array: number of nX3 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.

%I A223213 #8 Jul 23 2025 03:52:14
%S A223213 60,918,15498,254694,4232586,70014654,1160465118,19217863458,
%T A223213 318374151654,5273531868834,87356475139362,1447024166557638,
%U A223213 23969667617068794,397050589780025454,6577043474587192446
%N A223213 3X3X3 triangular graph coloring a rectangular array: number of nX3 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 A223213 Column 3 of A223218
%H A223213 R. H. Hardin, <a href="/A223213/b223213.txt">Table of n, a(n) for n = 1..210</a>
%F A223213 Empirical: a(n) = 10*a(n-1) +118*a(n-2) -120*a(n-3) -577*a(n-4) +380*a(n-5) +504*a(n-6) -16*a(n-8).
%F A223213 Empirical g.f.: -6*x*(-10-53*x+127*x^2+235*x^3-277*x^4-258*x^5+4*x^6+8*x^7) / ( 1-10*x-118*x^2+120*x^3+577*x^4-380*x^5-504*x^6+16*x^8 ). - _R. J. Mathar_, May 21 2018
%e A223213 Some solutions for n=3
%e A223213 ..1..4..2....2..5..2....5..2..5....4..1..3....4..5..4....1..2..1....4..1..2
%e A223213 ..4..5..4....5..2..1....4..1..4....2..4..1....1..4..1....2..1..4....2..4..5
%e A223213 ..3..4..1....2..1..3....3..4..3....4..1..4....4..1..2....1..4..5....4..5..4
%K A223213 nonn
%O A223213 1,1
%A A223213 _R. H. Hardin_ Mar 18 2013