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.

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

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: A325812 A323652 A375235 * A109510 A034715 A294730

Adjacent sequences: A223343 A223344 A223345 * A223347 A223348 A223349

Keyword

nonn

Author

R. H. Hardin, Mar 19 2013

Status

approved