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A223253 Two-loop graph coloring a rectangular array: number of nX6 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 A223253 #6 Jul 23 2025 03:55:22
%S A223253 528,22388,1382228,93770308,6581646956,465277782336,32969186423292,
%T A223253 2337308796813336,165726502883851820,11751198778793357708,
%U A223253 833253057095552710328,59084372484837842357680,4189562192845318714550284
%N A223253 Two-loop graph coloring a rectangular array: number of nX6 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 A223253 Column 6 of A223255
%H A223253 R. H. Hardin, <a href="/A223253/b223253.txt">Table of n, a(n) for n = 1..210</a>
%F A223253 Empirical: a(n) = 85*a(n-1) -629*a(n-2) -31878*a(n-3) +383553*a(n-4) +1511513*a(n-5) -30275140*a(n-6) +13466360*a(n-7) +868562158*a(n-8) -1847634768*a(n-9) -9913428815*a(n-10) +32760286161*a(n-11) +38433165015*a(n-12) -223138155283*a(n-13) +39999637275*a(n-14) +633199628532*a(n-15) -503848981336*a(n-16) -699539358490*a(n-17) +910162467392*a(n-18) +144242579620*a(n-19) -523191556820*a(n-20) +110096749408*a(n-21) +74380599616*a(n-22) -21347917248*a(n-23) -1345719744*a(n-24) for n>25
%e A223253 Some solutions for n=3
%e A223253 ..1..0..4..0..1..2....1..0..2..1..2..0....0..1..2..0..3..0....0..1..0..4..3..0
%e A223253 ..0..3..0..4..0..1....0..2..0..2..0..3....1..2..0..3..0..4....1..0..4..3..0..4
%e A223253 ..1..0..1..0..4..0....2..0..3..0..3..0....2..0..3..0..1..0....0..1..0..4..3..0
%K A223253 nonn
%O A223253 1,1
%A A223253 _R. H. Hardin_ Mar 18 2013