cp's OEIS Frontend

A223346 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.

%I A223346 #15 Jan 05 2021 02:40:21
%S A223346 6,12,28,60,140,300,700,1500,3500,7500,17500,37500,87500,187500,
%T A223346 437500,937500,2187500,4687500,10937500,23437500,54687500,117187500,
%U A223346 273437500,585937500,1367187500,2929687500,6835937500,14648437500,34179687500
%N A223346 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 A223346 Column 1 of A223352.
%H A223346 R. H. Hardin, <a href="/A223346/b223346.txt">Table of n, a(n) for n = 1..210</a>
%F A223346 From _Pierre-Louis Giscard_, May 17 2013: (Start)
%F A223346 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 A223346 G.f: 2*(x^2-6*x-3)/(5*x^2-1).
%F A223346 E.g.f.: (2/5)*(1 + 14*cosh(sqrt(5)*x) + 6*sqrt(5)*sinh(sqrt(5)*x)).  (End)
%e A223346 Some solutions for n=3:
%e A223346   3  1  5  1  4  3  0  0  1  2  3  4  0  2  2  2
%e A223346   1  4  2  4  2  1  2  2  0  0  1  2  1  4  4  0
%e A223346   0  2  0  1  0  4  5  0  2  1  3  5  4  1  2  2
%t A223346 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 A223346 nonn
%O A223346 1,1
%A A223346 _R. H. Hardin_, Mar 19 2013