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A223214 3X3X3 triangular graph coloring a rectangular array: number of nX4 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 A223214 #6 Jul 23 2025 03:52:21
%S A223214 192,6642,254694,9640008,367156350,13964418774,531419938920,
%T A223214 20220127602030,769404277676466,29276398278326448,1113995137856350842,
%U A223214 42388505934881462730,1612921387627093865328,61373120006749414194594
%N A223214 3X3X3 triangular graph coloring a rectangular array: number of nX4 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 A223214 Column 4 of A223218
%H A223214 R. H. Hardin, <a href="/A223214/b223214.txt">Table of n, a(n) for n = 1..210</a>
%F A223214 Empirical: a(n) = 36*a(n-1) +219*a(n-2) -5538*a(n-3) +3051*a(n-4) +141678*a(n-5) -180657*a(n-6) -980802*a(n-7) +1136403*a(n-8) +1765044*a(n-9) -1679697*a(n-10) -991440*a(n-11) +763668*a(n-12) +60264*a(n-13) -77760*a(n-14) +7776*a(n-15)
%e A223214 Some solutions for n=3
%e A223214 ..3..1..2..4....0..1..4..3....1..3..4..2....4..5..2..1....3..1..0..1
%e A223214 ..4..2..0..2....1..2..5..4....3..1..2..5....3..4..1..4....1..4..1..4
%e A223214 ..5..4..1..4....2..5..4..3....1..0..1..2....1..2..0..2....3..1..2..5
%K A223214 nonn
%O A223214 1,1
%A A223214 _R. H. Hardin_ Mar 18 2013