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A V-Toothpick is formed by two half toothpick with a 120 degree angle, as a V.
On the infinite triangular grid, we start at round 0 with no V-Toothpicks.
At round 1 we place a V-Toothpick anywhere in the plane.
At round 2 we place two other V-Toothpicks. Note that, after round 2, in the sieve there are three V-Toothpick, with seven 120 degree angles and a 240 degree angle.
At round 3 we place four other V-Toothpicks.
And so on...
The sieve looks like an unfinished honeycomb.
The sequence gives the number of V-Toothpicks after n rounds. A161207 (the first differences) gives the number added at the n-th round.
See the entry A139250 for more information about the toothpick process and the toothpick propagation.
Note that, on the infinite triangular grid, a V-Toothpick can be represented as a polyedge with two components. In this case, at n-th round, the sieve is a polyedge with 2*a(n) components.
In the sieve we can see distinct polygons with side length equal to 1, for example:
- Regular hexagons ............ (with 1 non covered grid point).
- Concave-convex decagons ..... (with 2 non covered grid points).
- Concave-convex dodecagons ... (with 4 non covered grid points).
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