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A223601 Petersen graph (8,2) coloring a rectangular array: number of 3Xn 0..15 arrays where 0..15 label nodes of a graph with edges 0,1 0,8 8,14 8,10 1,2 1,9 9,15 9,11 2,3 2,10 10,12 3,4 3,11 11,13 4,5 4,12 12,14 5,6 5,13 13,15 6,7 6,14 7,0 7,15 and every array movement to a horizontal, diagonal or antidiagonal neighbor moves along an edge of this graph.

%I A223601 #6 Jul 23 2025 04:17:11
%S A223601 4096,1376,16192,122608,1124064,9902320,90390720,827854448,7658651360,
%T A223601 71165672752,663933249024,6209221918896,58174002355232,
%U A223601 545677201489648,5122736643803840,48118345117470448,452153378054341216
%N A223601 Petersen graph (8,2) coloring a rectangular array: number of 3Xn 0..15 arrays where 0..15 label nodes of a graph with edges 0,1 0,8 8,14 8,10 1,2 1,9 9,15 9,11 2,3 2,10 10,12 3,4 3,11 11,13 4,5 4,12 12,14 5,6 5,13 13,15 6,7 6,14 7,0 7,15 and every array movement to a horizontal, diagonal or antidiagonal neighbor moves along an edge of this graph.
%C A223601 Row 3 of A223599
%H A223601 R. H. Hardin, <a href="/A223601/b223601.txt">Table of n, a(n) for n = 1..210</a>
%F A223601 Empirical: a(n) = 13*a(n-1) +3*a(n-2) -437*a(n-3) +544*a(n-4) +3614*a(n-5) -6064*a(n-6) -6480*a(n-7) +14240*a(n-8) -416*a(n-9) -7296*a(n-10) +2304*a(n-11) for n>12
%e A223601 Some solutions for n=3
%e A223601 ..7.15..9...10.12.14....5..6.14...12.14.12....6..7..0...13.15.13....7..0..8
%e A223601 .13.15.13...14.12.14....7..6..5...12..4.12...15..7..6...13.15..7....1..0..7
%e A223601 .13.11..9...14.12.14...14..6.14...12.14.12...15..7..6....7.15..9....1..0..7
%K A223601 nonn
%O A223601 1,1
%A A223601 _R. H. Hardin_ Mar 23 2013