A161423 -id:A161423 - 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