OFFSET
0,2
COMMENTS
LINKS
Nathaniel Johnston, Table of n, a(n) for n = 0..200
Nathaniel Johnston, C program for computing terms
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.]
Nathaniel Johnston, The Q-Toothpick Cellular Automaton
N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS
EXAMPLE
On the infinite square grid at stage 0 we start with no Q-toothpicks.
At stage 1 we place two opposite Q-toothpicks centered at (0,0). One of the Q-toothpicks lies on the first quadrant with its endpoints at (0,1) and (1,0). The other Q-toothpick lies on the third quadrant with its endpoints at (0,-1) and (-1,0). So a(1) = 2. There are 4 exposed endpoints.
At stage 2 we place 6 Q-toothpicks, so a(2) = 2+6 = 8.
At stage 3 we place 8 Q-toothpicks, so a(3) = 8+8 = 16.
At stage 4 we place 14 Q-toothpicks, so a(4) = 16+14 = 30.
After 4 stages in the Q-toothpick structure there are 1 circle, 2 "heads" and 12 exposed endpoints.
CROSSREFS
KEYWORD
nonn
AUTHOR
Omar E. Pol, Mar 30 2011
EXTENSIONS
a(15) - a(47) from Nathaniel Johnston, Apr 15 2011
STATUS
approved