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This sequence is a E-Toothpick sequence (A161328) but starting from opposite two E-Toothpicks.
On the infinite triangular grid, we start at round 0 with no E-Toothpicks.
At round 1 we place opposite two E-Toothpicks, as a star with six endpoints, anywhere in the plane.
At round 2 we place six other E-Toothpicks.
At round 3 we place six other E-Toothpicks.
And so on...
See the special rule for E-Toothpick sequences in the entry A161328.
The sequence gives the number of E-Toothpicks after n rounds. A161331 (the first differences) gives the number added at the nth round.
See the entry A139250 for more information about the toothpick process and the toothpick propagation.
Note that, on the infinite triangular grid, a E-Toothpick can be represented as a polyedge with three components. In this case, at nth round, the sieve is a polyedge with 3*a(n) components.
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