A161413 -id:A161413 - cp's OEIS frontend

A161412 V-toothpick sequence starting at the corner of an infinite square from which protrudes a half toothpick with an angle = Pi/6.

0, 1, 2, 3, 5, 9, 12, 15, 19, 25, 29, 34, 39, 49, 58, 63

Offset: 0

Omar E. Pol, Jun 10 2009

The sequence gives the number of V-toothpicks in the structure after n rounds. A161413 (the first differences) gives the number added at the n-th round.

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

V-toothpick sequence: A161206.

Cf. A139250, A160120, A160406, A161328, A161413.

A355311 Number of V-toothpicks added at n-th stage to the V-toothpick structure of A355310.

Original entry on oeis.org

1, 2, 4, 6, 8, 6, 10, 14, 18, 10, 10, 14, 20, 18, 24, 36, 44, 22

Offset: 1

Jean Hoffmann and Omar E. Pol, Jul 20 2022

An idea from Jean Hoffmann.

			Written as an irregular triangle in which the row lengths give 1 together with A011782 the sequence begins:
   1;
   2;
   4;
   6,  8;
   6, 10, 14, 18;
  10, 10, 14, 20, 18, 24, 36, 44;
   ...

First differences of A355310.

Cf. A011782, A139251, A160121, A161207, A161413, A161421, A296612, A299477, A299479.

cp's OEIS Frontend

A161412 V-toothpick sequence starting at the corner of an infinite square from which protrudes a half toothpick with an angle = Pi/6.

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