A177240 Number of K-toothpicks after n stages of 3-D K-toothpick structure defined in Comments.

0, 1, 5, 9, 25, 29, 45

Offset: 0

Author

Omar E. Pol, May 05 2010

Keywords

• more
• nonn

Comments

We are in 3-D. Here the polytoothpick is a K-toothpick. The K-toothpick has 4 components or line segments, a central point and 4 endpoints, as a tetrapod but without volume. The K-toothpick endpoints coincide with the vertices of a regular tetrahedron.

It appears that this is a three-dimensional version of A160120, but with K-toothpicks, not with Y-toothpick.

The first differences are in the entry A177241.

For the toothpick mechanism see A139250 and A160120.

Question: Is this the same as A116520? (To answer the question we need a program because the structure is hard to visualize).

Links

• David Applegate, Omar E. Pol and N. J. A. Sloane, The Toothpick Sequence and Other Sequences from Cellular Automata, Congressus Numerantium, Vol. 206 (2010), 157-191. [There is a typo in Theorem 6: (13) should read u(n) = 4.3^(wt(n-1)-1) for n >= 2.]
• N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS

Crossrefs

Cf. A102376, A116520, A139250, A160120, A177241.

Extensions

Edited by Omar E. Pol, May 07 2010