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%I #6 Feb 24 2021 02:48:19
%S 0,1,5,9,25,29,45
%N Number of K-toothpicks after n stages of 3-D K-toothpick structure defined in Comments.
%C 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.
%C It appears that this is a three-dimensional version of A160120, but with K-toothpicks, not with Y-toothpick.
%C The first differences are in the entry A177241.
%C For the toothpick mechanism see A139250 and A160120.
%C Question: Is this the same as A116520? (To answer the question we need a program because the structure is hard to visualize).
%H David Applegate, Omar E. Pol and N. J. A. Sloane, <a href="/A000695/a000695_1.pdf">The Toothpick Sequence and Other Sequences from Cellular Automata</a>, 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.]
%H N. J. A. Sloane, <a href="/wiki/Catalog_of_Toothpick_and_CA_Sequences_in_OEIS">Catalog of Toothpick and Cellular Automata Sequences in the OEIS</a>
%Y Cf. A102376, A116520, A139250, A160120, A177241.
%K more,nonn
%O 0,3
%A _Omar E. Pol_, May 05 2010
%E Edited by _Omar E. Pol_, May 07 2010
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