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%I #15 Jan 05 2021 02:40:21
%S 6,12,28,60,140,300,700,1500,3500,7500,17500,37500,87500,187500,
%T 437500,937500,2187500,4687500,10937500,23437500,54687500,117187500,
%U 273437500,585937500,1367187500,2929687500,6835937500,14648437500,34179687500
%N 3 X 3 X 3 triangular graph without horizontal edges coloring a rectangular array: number of n X 1 0..5 arrays where 0..5 label nodes of a graph with edges 0,1 0,2 1,3 1,4 2,4 2,5 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.
%C Column 1 of A223352.
%H R. H. Hardin, <a href="/A223346/b223346.txt">Table of n, a(n) for n = 1..210</a>
%F From _Pierre-Louis Giscard_, May 17 2013: (Start)
%F a(n) = 2*5^((1/2)*(n-3))*(15 + 7*sqrt(5) + (-1)^n*(-15 + 7*sqrt(5))) for n > 0, a(0)=6.
%F G.f: 2*(x^2-6*x-3)/(5*x^2-1).
%F E.g.f.: (2/5)*(1 + 14*cosh(sqrt(5)*x) + 6*sqrt(5)*sinh(sqrt(5)*x)). (End)
%e Some solutions for n=3:
%e 3 1 5 1 4 3 0 0 1 2 3 4 0 2 2 2
%e 1 4 2 4 2 1 2 2 0 0 1 2 1 4 4 0
%e 0 2 0 1 0 4 5 0 2 1 3 5 4 1 2 2
%t Table[2*5^(1/2*(n - 3))*(15 + 7*Sqrt[5] + (-1)^n*(-15 + 7*Sqrt[5])), {n,1,20}] (* _Pierre-Louis Giscard_, May 17 2013 *)
%K nonn
%O 1,1
%A _R. H. Hardin_, Mar 19 2013
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