A151566 Leftist toothpicks (see Comments for definition).

0, 1, 2, 4, 6, 8, 10, 14, 18, 20, 22, 26, 30, 34, 38, 46, 54, 56, 58, 62, 66, 70, 74, 82, 90, 94, 98, 106, 114, 122, 130, 146, 162, 164, 166, 170, 174, 178, 182, 190, 198, 202, 206, 214, 222, 230, 238, 254, 270, 274, 278, 286, 294, 302, 310, 326, 342, 350, 358, 374, 390, 406

Offset: 0

Author

N. J. A. Sloane, May 23 2009

Keywords

• nonn
• easy

Comments

Similar to A139250, except that when we add toothpicks to horizontal toothpicks, we only add them at the left-hand end.

Sequence gives total number of toothpicks in the n-th generation. First differences are in A060632.

This is equivalent to the Sierpinski triangle A047999. Each inverted T formed by two toothpicks is equivalent to a triangle in the Sierpinski sieve. See Gould's sequence A001316. [From Omar E. Pol, May 23 2009]

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000
• 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. A001316, A006046.

Formula

a(2n) = 2*A006046(n), a(2n+1) = a(2n) + A001316(n) = 2*A006046(n) + A001316(n).

G.f.: (x*(1+x)/(1-x)) * Product_{k>0} (1 + 2 * x^(2^k)). - Seiichi Manyama, Oct 12 2019