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
G.f.: (x*(1+x)/(1-x)) * Product_{k>0} (1 + 2 * x^(2^k)). - Seiichi Manyama, Oct 12 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, May 23 2009
STATUS
approved