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A223425
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5 X 5 X 5 triangular graph without horizontal edges coloring a rectangular array: number of n X 1 0..14 arrays where 0..14 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 6,10 6,11 7,11 7,12 8,12 8,13 9,13 9,14 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.
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%I #8 Aug 20 2018 14:37:30
%S 15,40,120,356,1088,3276,10052,30380,93296,282240,866908,2623264,
%T 8057756,24384556,74901596,226673608,696270792,2107127204,6472442928,
%U 19587617308,60167110388,182084416108,559307110768,1692637810416,5199260845212
%N 5 X 5 X 5 triangular graph without horizontal edges coloring a rectangular array: number of n X 1 0..14 arrays where 0..14 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 6,10 6,11 7,11 7,12 8,12 8,13 9,13 9,14 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.
%C Column 1 of A223432.
%H R. H. Hardin, <a href="/A223425/b223425.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 14*a(n-2) - 49*a(n-4) + 49*a(n-6) for n>7.
%F Empirical g.f.: x*(15 + 40*x - 90*x^2 - 204*x^3 + 143*x^4 + 252*x^5 - 35*x^6) / ((1 - 7*x^2 + 7*x^3)*(1 - 7*x^2 - 7*x^3)). - _Colin Barker_, Aug 20 2018
%e Some solutions for n=3:
%e ..5....1....8....3....2....2...10....6....4....7....2....7....0....2....4....8
%e ..8....4....5....7....5....4....6....3....8....3....0....3....2....4....2....5
%e .13....2....8...12....2....2....3....6....5....1....2....7....4....8....4....9
%Y Cf. A223432.
%K nonn
%O 1,1
%A _R. H. Hardin_, Mar 20 2013
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