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A223346 3X3X3 triangular graph without horizontal edges coloring a rectangular array: number of nX1 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: A068412 A183026 A146005 * 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 December 12 15:01 EST 2017. Contains 295939 sequences.