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

0,3

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

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

Crossrefs

Cf. A001316, A006046.

Sequence in context: A242418 A191146 A220850 * A160406 A113293 A080431

Adjacent sequences: A151563 A151564 A151565 * A151567 A151568 A151569

Keyword

nonn,easy

Author

N. J. A. Sloane, May 23 2009

Status

approved