A223408 - OEIS

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A223408

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.

10, 24, 66, 176, 486, 1312, 3622, 9792, 27030, 73088, 201750, 545536, 1505878, 4071936, 11240022, 30393344, 83896662, 226859008, 626213206, 1693298688, 4674118998, 12638953472, 34888099158, 94338433024, 260408317270

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Column 1 of A223415.

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..210

FORMULA

Empirical: a(n) = 9*a(n-2) - 12*a(n-4) + 4*a(n-6).

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

EXAMPLE

Some solutions for n=3: