A194700 D-toothpick sequence of the third kind (see Comments lines for definition).

0, 1, 5, 13, 29, 51, 75, 97, 137, 177, 209, 241, 297, 371, 467, 533

Offset: 0

Author

Omar E. Pol, Sep 02 2011

Keywords

• nonn
• more

Comments

This is a cellular automaton of forking paths to 135 degrees which uses elements of three sizes: toothpicks of length 1, D-toothpicks of length 2^(1/2) and D-toothpicks of length 2^(1/2)/2. Toothpicks are placed in horizontal or vertical direction. D-toothpicks are placed in diagonal direction. Toothpicks and D-toothpicks are connected by their endpoints.

On the infinite square grid we start with no elements.

At stage 1, place a single D-toothpick on the paper, in diagonal direction.

The rule for adding new elements is as follows. Each exposed endpoint of the elements of the old generation must be touched by the two endpoints of two elements of the new generation such that the angle between the old element and each new element is equal to 135 degrees. Intersections and overlapping are prohibited.

This toothpick structure is very similar to A194270, but here there are no toothpicks endpoints that remain exposed forever.

Links

• David Applegate, The movie version
• N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS
• Index entries for sequences related to toothpick sequences

Crossrefs

Cf. A139250, A194270.