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A223351 3X3X3 triangular graph without horizontal edges coloring a rectangular array: number of nX7 0..5 arrays where 0..5 label nodes of a graph with edges 0,1 0,2 1,3 1,4 2,4 2,5 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.

%I A223351 #6 Jul 23 2025 04:02:17
%S A223351 700,102124,17970056,3013692516,537001573656,90254934876620,
%T A223351 16086247351158920,2703767114101083332,481898364416857970648,
%U A223351 80997279330454571309932,14436325294811073087488072
%N A223351 3X3X3 triangular graph without horizontal edges coloring a rectangular array: number of nX7 0..5 arrays where 0..5 label nodes of a graph with edges 0,1 0,2 1,3 1,4 2,4 2,5 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.
%C A223351 Column 7 of A223352
%H A223351 R. H. Hardin, <a href="/A223351/b223351.txt">Table of n, a(n) for n = 1..210</a>
%F A223351 Empirical: a(n) = 32411*a(n-2) -75899152*a(n-4) +72830232672*a(n-6) -37138383320832*a(n-8) +11267693571807232*a(n-10) -2156486785001701376*a(n-12) +268134896419496787968*a(n-14) -21861109815107756490752*a(n-16) +1158919426002765454770176*a(n-18) -38882391728037610366435328*a(n-20) +785674063552141870019641344*a(n-22) -8851677936996895344820224000*a(n-24) +50604844225802475480926912512*a(n-26) -142492256277654023889441783808*a(n-28) +199942375039742209972462682112*a(n-30) -136858193061759279004901179392*a(n-32) +42178458483591906497874886656*a(n-34) -4502039752244879046605799424*a(n-36)
%e A223351 Some solutions for n=3
%e A223351 ..0..1..0..2..0..1..3....0..1..0..2..0..2..4....0..1..0..1..0..1..0
%e A223351 ..1..3..1..0..2..4..1....1..0..1..0..1..0..2....1..0..1..4..2..0..2
%e A223351 ..0..1..3..1..0..2..0....0..2..4..1..4..2..5....0..2..0..1..4..1..4
%K A223351 nonn
%O A223351 1,1
%A A223351 _R. H. Hardin_ Mar 19 2013