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A187216 Q-toothpick sequence starting with two opposite Q-toothpicks centered at the same grid point. 2
0, 2, 8, 16, 30, 52, 82, 104, 142, 196, 266, 288, 326, 380, 450, 504, 606, 756, 890, 912, 950, 1004, 1074, 1128, 1230, 1380, 1514, 1568, 1670, 1820, 1986, 2168, 2494, 2900, 3162, 3184, 3222, 3276, 3346, 3400, 3502, 3652, 3786, 3840, 3942, 4092, 4258, 4440 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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.

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

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

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

Sequence in context: A194643 A136514 A077071 * A210729 A077666 A232358

Adjacent sequences:  A187213 A187214 A187215 * A187217 A187218 A187219

KEYWORD

nonn

AUTHOR

Omar E. Pol, Mar 30 2011

EXTENSIONS

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

STATUS

approved

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Last modified August 28 00:41 EDT 2015. Contains 261101 sequences.