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%I #7 Aug 20 2018 08:37:37
%S 10,24,66,176,486,1312,3622,9792,27030,73088,201750,545536,1505878,
%T 4071936,11240022,30393344,83896662,226859008,626213206,1693298688,
%U 4674118998,12638953472,34888099158,94338433024,260408317270
%N 4 X 4 X 4 triangular graph without horizontal edges coloring a rectangular array: number of n X 1 0..9 arrays where 0..9 label nodes of a graph with edges 0,1 0,2 1,3 1,4 2,4 2,5 3,6 3,7 4,7 4,8 5,8 5,9 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.
%C Column 1 of A223415.
%H R. H. Hardin, <a href="/A223408/b223408.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 9*a(n-2) - 12*a(n-4) + 4*a(n-6).
%F Empirical g.f.: 2*x*(5 + 12*x - 12*x^2 - 20*x^3 + 6*x^4 + 8*x^5) / ((1 - x)*(1 + x)*(1 + 2*x - 2*x^2)*(1 - 2*x - 2*x^2)). - _Colin Barker_, Aug 20 2018
%e Some solutions for n=3:
%e ..1....7....4....4....8....2....5....4....1....2....4....4....3....4....1....6
%e ..4....4....7....8....4....0....2....2....0....4....8....1....6....2....4....3
%e ..1....8....3....5....7....1....4....0....1....8....4....0....3....5....2....1
%Y Cf. A223415.
%K nonn
%O 1,1
%A _R. H. Hardin_, Mar 20 2013
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