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A161210 Toothpick sequence starting at the outside corner of an infinite cube from which protudes a half toothpick. 4
0, 1, 3, 7, 14, 21, 28 (list; graph; refs; listen; history; text; internal format)



The sequence gives the number of toothpicks after n rounds. A161211 (the first differences) gives the number added at the n-th round.

This structure is a three-dimensional version of the toothpick structure of A153006.

Toothpicks are placed following a rotation of axes: x,y,z,x,y,z,... and so on.

See A139250 and A160160 for more information about the toothpick sequences.


Table of n, a(n) for n=0..6.

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


Cf. A139250, A152980, A153006, A160160, A161211, A161212, A161214, A161216.

Sequence in context: A310275 A310276 A310277 * A256059 A258434 A249341

Adjacent sequences:  A161207 A161208 A161209 * A161211 A161212 A161213




Omar E. Pol, Jun 06 2009



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Last modified July 26 22:49 EDT 2021. Contains 346300 sequences. (Running on oeis4.)