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A223422 3-level binary fanout graph coloring a rectangular array: number of nX7 0..6 arrays where 0..6 label nodes of a graph with edges 0,1 1,3 1,4 0,2 2,5 2,6 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.

%I A223422 #6 Jul 23 2025 04:08:12
%S A223422 416,18464,1033328,50097024,2844612736,139114196992,7939011165696,
%T A223422 389154431528960,22244132907945984,1091144538683604992,
%U A223422 62401586754017968128,3061680318925083639808,175122575873489263525888
%N A223422 3-level binary fanout graph coloring a rectangular array: number of nX7 0..6 arrays where 0..6 label nodes of a graph with edges 0,1 1,3 1,4 0,2 2,5 2,6 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.
%C A223422 Column 7 of A223423
%H A223422 R. H. Hardin, <a href="/A223422/b223422.txt">Table of n, a(n) for n = 1..210</a>
%F A223422 Empirical: a(n) = 4144*a(n-2) -4233568*a(n-4) +1423446528*a(n-6) -216571051008*a(n-8) +17498453049344*a(n-10) -823976834072576*a(n-12) +23806610175950848*a(n-14) -433179956841807872*a(n-16) +5014404982720430080*a(n-18) -36922985056839925760*a(n-20) +171827754849678655488*a(n-22) -499189157380780720128*a(n-24) +886405116754355290112*a(n-26) -927140136557417070592*a(n-28) +537868927709415997440*a(n-30) -158472804425401368576*a(n-32) +20342196566879109120*a(n-34) -788129934789836800*a(n-36)
%e A223422 Some solutions for n=3
%e A223422 ..0..1..4..1..3..1..3....0..1..0..1..0..2..6....0..1..3..1..4..1..0
%e A223422 ..1..3..1..3..1..3..1....1..0..2..0..2..0..2....1..0..1..3..1..0..1
%e A223422 ..3..1..3..1..3..1..4....3..1..0..2..5..2..0....0..1..3..1..3..1..0
%K A223422 nonn
%O A223422 1,1
%A A223422 _R. H. Hardin_ Mar 20 2013