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
Keywords
Examples
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
Links
- R. H. Hardin, Table of n, a(n) for n = 1..210
Programs
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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 *)
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)
Comments