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A223251 Two-loop graph coloring a rectangular array: number of n X 4 0..4 arrays where 0..4 label nodes of a graph with edges 0,1 1,2 2,0 0,3 3,4 4,0 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.

%I A223251 #8 Aug 18 2018 08:43:19
%S A223251 80,1076,17828,307144,5359892,93770308,1641741608,28748561780,
%T A223251 503440061060,8816254627208,154390919319636,2703707386173764,
%U A223251 47347570829880040,829155025056272692,14520239405020681988
%N A223251 Two-loop graph coloring a rectangular array: number of n X 4 0..4 arrays where 0..4 label nodes of a graph with edges 0,1 1,2 2,0 0,3 3,4 4,0 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.
%C A223251 Column 4 of A223255.
%H A223251 R. H. Hardin, <a href="/A223251/b223251.txt">Table of n, a(n) for n = 1..210</a>
%F A223251 Empirical: a(n) = 20*a(n-1) - 28*a(n-2) - 299*a(n-3) + 436*a(n-4) + 476*a(n-5) - 460*a(n-6) for n>7.
%F A223251 Empirical g.f.: 4*x*(20 - 131*x - 363*x^2 + 1158*x^3 + 760*x^4 - 1036*x^5 + 24*x^6) / (1 - 20*x + 28*x^2 + 299*x^3 - 436*x^4 - 476*x^5 + 460*x^6). - _Colin Barker_, Aug 18 2018
%e A223251 Some solutions for n=3:
%e A223251 ..4..0..4..3....2..0..3..0....0..4..0..2....0..3..0..1....3..0..3..0
%e A223251 ..0..4..3..4....0..3..0..3....2..0..2..0....1..0..4..0....0..3..0..4
%e A223251 ..1..0..4..3....3..0..2..0....0..3..0..1....0..4..0..4....4..0..2..0
%Y A223251 Cf. A223255.
%K A223251 nonn
%O A223251 1,1
%A A223251 _R. H. Hardin_, Mar 18 2013