A194432 D-toothpick sequence starting with a cross formed by 4 toothpicks.

0, 4, 12, 28, 44, 60, 88, 136, 168, 184, 216

Offset: 0

Author

Omar E. Pol, Sep 03 2011

Keywords

• nonn
• more

Comments

On the infinite square grid we start with no toothpicks.

At stage 1, we place a cross, centered at the origin, formed by 2 vertical toothpicks and 2 horizontal toothpicks of length 1. At stage 2, we place 8 D-toothpicks of length sqrt(2). At stage 3, we place 16 toothpicks of length 1. And so on.

The sequence gives the number of toothpicks and D-toothpicks in the structure after n-th stage. The first differences (A194433) give the number of toothpicks and D-toothpicks added at n-th stage.

Apparently this cellular automaton has a fractal (or fractal-like) behavior related to power of 2, similar to A194270 and very similar to A194434. The octagonal structure contains a large number of distinct polygonal shapes. For more information see A194270, A194440 and A194442.

Links

• 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, A194433, A194434, A194440, A194442.