A334555 - OEIS

A334555

Number of Eulerian orientations in the triangular grid graph with n vertices on each side.

1, 2, 10, 126, 4058, 335880, 71670920, 39502865556, 56311864852276, 207801222582652912, 1986359616920243022736, 49208826219541189516584984, 3160589584425292542210483325768, 526456712955511606070610013564727680, 227473288747399377932382913309432126945664

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

OFFSET

1,2

COMMENTS

An Eulerian orientation of a graph is an orientation of the edges such that every vertex has in-degree equal to out-degree.

For n > 1, all values are divisible by 2 since reversing the orientation of every arc in a solution gives another solution.

LINKS

Table of n, a(n) for n=1..15.

Eric Weisstein's World of Mathematics, Triangular Grid Graph

EXAMPLE

a(2) = 2 since there are two ways to orient the edges of a triangle so that edge vertex has in-degree equal to out-degree.

CROSSREFS