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A223594 Petersen graph (8,2) coloring a rectangular array: number of n X 3 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 A223594 #8 Aug 21 2018 10:04:26
%S A223594 144,1504,16192,176224,1931968,21308000,236213312,2629972704,
%T A223594 29389265856,329426847840,3702023397952,41690675717344,
%U A223594 470324275582912,5313486488316000,60099803562912832,680431871048616672
%N A223594 Petersen graph (8,2) coloring a rectangular array: number of n X 3 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 A223594 Column 3 of A223599.
%H A223594 R. H. Hardin, <a href="/A223594/b223594.txt">Table of n, a(n) for n = 1..210</a>
%F A223594 Empirical: a(n) = 23*a(n-1) - 153*a(n-2) + 217*a(n-3) + 258*a(n-4) - 456*a(n-5) - 104*a(n-6) + 192*a(n-7).
%F A223594 Empirical g.f.: 16*x*(9 - 113*x + 227*x^2 + 167*x^3 - 458*x^4 - 64*x^5 + 192*x^6) / (1 - 23*x + 153*x^2 - 217*x^3 - 258*x^4 + 456*x^5 + 104*x^6 - 192*x^7). - _Colin Barker_, Aug 21 2018
%e A223594 Some solutions for n=3:
%e A223594 ..4..5..4....9..1..9....2.10..8....5..6..5....9.15..9....5.13..5....8.10.12
%e A223594 ..4..5..4....0..1..2....8.10..8....5..4..5...13.11..9...11.13..5....2.10..2
%e A223594 ..4..5..4....0..1..9....8.14..8....3..4..3...13.15..9...15.13..5....2.10.12
%Y A223594 Cf. A223599.
%K A223594 nonn
%O A223594 1,1
%A A223594 _R. H. Hardin_, Mar 23 2013