0,2

The sequence gives the number of Q-toothpicks in the structure after n-th stage.

A187217 (the first differences) gives the number of Q-toothpicks added at n-th stage.

Note that in the Q-toothpick structure sometimes there is also an internal growth of Q-toothpicks.

For more information see A187210.

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

Nathaniel Johnston, The Q-Toothpick Cellular Automaton

N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS

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.

Cf. A139250, A160120, A160164, A187210, A187212, A187217, A187220.

Sequence in context: A327329 A136514 A077071 * A210729 A294534 A294542

Adjacent sequences: A187213 A187214 A187215 * A187217 A187218 A187219

Omar E. Pol, Mar 30 2011

a(15) - a(47) from Nathaniel Johnston, Apr 15 2011

approved