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A223250 Two-loop graph coloring a rectangular array: number of n X 3 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 A223250 #10 May 03 2014 13:24:08
%S A223250 32,236,2172,17828,166892,1382228,12894316,107283636,996653548,
%T A223250 8326150836,77047324460,646086687220,5957011569772,50127570610868,
%U A223250 460630428892844,3888717399278196,35622664419652844,301636706357260340
%N A223250 Two-loop graph coloring a rectangular array: number of n X 3 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 A223250 Column 3 of A223255.
%H A223250 R. H. Hardin, <a href="/A223250/b223250.txt">Table of n, a(n) for n = 1..210</a>
%F A223250 Empirical: a(n) = 2*a(n-1) +75*a(n-2) -126*a(n-3) -70*a(n-4) +48*a(n-5).
%F A223250 Empirical g.f.: -4*x*(78*x^4 -46*x^3 -175*x^2 +43*x +8) / (48*x^5 -70*x^4 -126*x^3 +75*x^2 +2*x -1). - _Colin Barker_, May 03 2014
%e A223250 Some solutions for n=3:
%e A223250 ..3..0..1....4..0..3....3..4..3....1..0..4....4..3..4....1..0..3....1..0..3
%e A223250 ..0..2..0....0..2..0....4..3..4....0..1..0....0..4..3....0..1..0....0..2..0
%e A223250 ..4..0..2....2..0..3....3..4..0....3..0..2....3..0..4....3..0..1....2..0..2
%K A223250 nonn
%O A223250 1,1
%A A223250 _R. H. Hardin_, Mar 18 2013