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A223434 Generalized Petersen graph (8,2) coloring a rectangular array: number of n X 2 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 or vertical neighbor moves along an edge of this graph.

%I A223434 #7 Mar 16 2018 07:23:54
%S A223434 48,256,1376,7424,40160,217600,1180256,6405888,34782688,188912640,
%T A223434 1026197344,5575016704,30289360608,164570543616,894181114976,
%U A223434 4858543170304,26399224399840,143442922485760,779415220762976
%N A223434 Generalized Petersen graph (8,2) coloring a rectangular array: number of n X 2 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 or vertical neighbor moves along an edge of this graph.
%C A223434 Column 2 of A223440.
%H A223434 R. H. Hardin, <a href="/A223434/b223434.txt">Table of n, a(n) for n = 1..210</a>
%F A223434 Empirical: a(n) = 8*a(n-1) - 11*a(n-2) - 16*a(n-3).
%F A223434 Empirical g.f.: 16*x*(3 - 8*x - 9*x^2) / (1 - 8*x + 11*x^2 + 16*x^3). - _Colin Barker_, Mar 16 2018
%e A223434 Some solutions for n=3:
%e A223434 ..6..5....8..0....3..4...11.13....7..0...11.13....9..1....1..0....1..9....1..9
%e A223434 .14..6....0..7....2..3...13.15...15..7...13.15....1..2....0..1....2..1....9.11
%e A223434 ..8.14....8..0....3..2...15.13....9.15...15..7....2..3....1..2....3..2....1..9
%Y A223434 Cf. A223440.
%K A223434 nonn
%O A223434 1,1
%A A223434 _R. H. Hardin_, Mar 20 2013