A172308 L-toothpick sequence in the first quadrant.

0, 1, 3, 5, 7, 11, 15, 17, 21, 27, 33, 41, 47, 59, 69, 75, 79, 85, 95, 107, 117, 131, 145, 161, 177, 195, 209, 225, 237, 257, 279, 287, 295, 311, 329, 345, 355, 371, 391, 415, 441, 477, 501, 533, 563, 603, 631, 655

Offset: 0

Author

Omar E. Pol, Feb 06 2010

Keywords

• nonn

Comments

The same as A172310 and A172304, but starting from half L-toothpick in the first quadrant.

Note that if n is odd then we add the small L-toothpicks to the structure, otherwise we add the large L-toothpicks to the structure.

We start at stage 0 with half L-toothpick: A segment from (0,0) to (1,1).

At stage 1 we place a small L-toothpick at the exposed toothpick end.

At stage 2 we place two large L-toothpicks.

At stage 3 we place two small L-toothpicks.

At stage 4 we place two large L-toothpicks.

And so on...

The sequence gives the number of L-toothpicks after n stages. A172309 (the first differences) gives the number of L-toothpicks added at the n-th stage.

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, A153000, A160120, A160170, A160172, A161206, A161328, A172304, A172305, A172306, A172307, A172309, A172310, A172311, A172312, A172313.

Extensions

a(17)-a(47) from Robert Price, Jun 17 2019