A161421 -id:A161421 - cp's OEIS frontend

A161420 V-toothpick sequence starting from a V-toothpick whose central point touch a straight line, as a V.

0, 1, 3, 5, 7, 11, 19, 25, 31, 39, 51, 59, 69, 79, 99, 117, 127, 143, 163, 171

Offset: 0

Omar E. Pol, Jun 10 2009

The sequence gives the number of V-toothpicks after n-th stages on hexagonal net. A161421 (the first differences) gives the number added at the n-th stage. See A161206 for more information.

Also, it appears this is a H-toothpick sequence in the first quadrant on the square grid, starting with a D-toothpick from the point (0,0). The sequence gives the number of toothpicks and D-toothpicks after n-th stage. A161421 (the first differences) gives the number added at the n-th stage. For more information see A182838.

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, A160120, A160406, A161206, A161328, A161412, A161421, A161422, A161423, A182832, A182838.

A161423 Primes in A161420.

Original entry on oeis.org

3, 5, 7, 11, 19, 31, 59, 79, 127, 163

Offset: 1

Omar E. Pol, Jun 10 2009

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. A139253, A161420, A161421.

Error in data corrected by D. S. McNeil, Aug 17 2010

a(10) from Michael S. Branicky, Jan 23 2023

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

A161420 V-toothpick sequence starting from a V-toothpick whose central point touch a straight line, as a V.

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A161423 Primes in A161420.

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

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