OFFSET
0,3
COMMENTS
On the infinite square grid, we start at round 0 drawing a straight line, with angle = Pi/4, from which protrudes a half toothpick.
At round 1 we place an orthogonal toothpick centered at the end.
In each subsequent round, for every exposed toothpick end, place an orthogonal toothpick centered at that end.
The sequence gives the number of toothpicks after n rounds.
See also A168113, the first differences.
For more information see A139250, which is the main entry for this sequence.
LINKS
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(n) = A160730(n)/2. [From Nathaniel Johnston, Mar 28 2011]
CROSSREFS
KEYWORD
nonn
AUTHOR
Omar E. Pol, Dec 07 2009
EXTENSIONS
Terms after a(34) from Nathaniel Johnston, Mar 28 2011
STATUS
approved