A161210 Toothpick sequence starting at the outside corner of an infinite cube from which protrudes a half toothpick.

0, 1, 3, 7, 14, 21, 28

Offset: 0

Author

Omar E. Pol, Jun 06 2009

Keywords

• more
• nonn

Comments

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.

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