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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. 1
6, 12, 28, 60, 140, 300, 700, 1500, 3500, 7500, 17500, 37500, 87500, 187500, 437500, 937500, 2187500, 4687500, 10937500, 23437500, 54687500, 117187500, 273437500, 585937500, 1367187500, 2929687500, 6835937500, 14648437500, 34179687500 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Column 1 of A223352.

LINKS

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

FORMULA

From Pierre-Louis Giscard, May 17 2013: (Start)

a(n) = 2*5^((1/2)*(n-3))*(15 + 7*sqrt(5) + (-1)^n*(-15 + 7*sqrt(5))) for n > 0, a(0)=6.

G.f: 2*(x^2-6*x-3)/(5*x^2-1).

E.g.f.: (2/5)*(1 + 14*cosh(sqrt(5)*x) + 6*sqrt(5)*sinh(sqrt(5)*x)).  (End)

EXAMPLE

Some solutions for n=3:

  3  1  5  1  4  3  0  0  1  2  3  4  0  2  2  2

  1  4  2  4  2  1  2  2  0  0  1  2  1  4  4  0

  0  2  0  1  0  4  5  0  2  1  3  5  4  1  2  2

MATHEMATICA

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 *)

CROSSREFS

Sequence in context: A146005 A325812 A323652 * A109510 A034715 A294730

Adjacent sequences:  A223343 A223344 A223345 * A223347 A223348 A223349

KEYWORD

nonn

AUTHOR

R. H. Hardin, Mar 19 2013

STATUS

approved

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Last modified March 5 11:57 EST 2021. Contains 341823 sequences. (Running on oeis4.)