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A223299
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4 X 4 X 4 triangular graph coloring a rectangular array: number of n X 2 0..9 arrays where 0..9 label nodes of a graph with edges 0,1 0,2 1,2 1,3 1,4 2,4 3,4 2,5 4,5 3,6 3,7 4,7 6,7 4,8 5,8 7,8 5,9 8,9 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.
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%I #8 Aug 19 2018 07:36:31
%S 36,324,3132,30564,298620,2918052,28515132,278649828,2722966524,
%T 26608833828,260021573820,2540931306084,24829985481084,
%U 242638664618916,2371065485035068,23170056359958756,226417834139125500
%N 4 X 4 X 4 triangular graph coloring a rectangular array: number of n X 2 0..9 arrays where 0..9 label nodes of a graph with edges 0,1 0,2 1,2 1,3 1,4 2,4 3,4 2,5 4,5 3,6 3,7 4,7 6,7 4,8 5,8 7,8 5,9 8,9 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.
%C Column 2 of A223305.
%H R. H. Hardin, <a href="/A223299/b223299.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 11*a(n-1) - 12*a(n-2).
%F Conjectures from _Colin Barker_, Aug 19 2018: (Start)
%F G.f.: 36*x*(1 - 2*x) / (1 - 11*x + 12*x^2).
%F a(n) = (3*2^(-n)*((11-sqrt(73))^n*(-1+sqrt(73)) + (1+sqrt(73))*(11+sqrt(73))^n)) / sqrt(73).
%F (End)
%e Some solutions for n=3:
%e ..0..2....2..0....8..9....5..4....7..8....0..2....4..8....3..4....3..4....1..3
%e ..2..5....4..1....4..5....9..8....4..7....1..0....2..5....4..2....1..2....0..1
%e ..5..2....1..2....1..4....5..9....7..3....0..2....1..2....8..4....2..1....1..3
%Y Cf. A223305.
%K nonn
%O 1,1
%A _R. H. Hardin_, Mar 19 2013
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