

A187216


Qtoothpick sequence starting with two opposite Qtoothpicks 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
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OFFSET

0,2


COMMENTS

The sequence gives the number of Qtoothpicks in the structure after nth stage.
A187217 (the first differences) gives the number of Qtoothpicks added at nth stage.
Note that in the Qtoothpick structure sometimes there is also an internal growth of Qtoothpicks.
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), 157191. [There is a typo in Theorem 6: (13) should read u(n) = 4.3^(wt(n1)1) for n >= 2.]
Nathaniel Johnston, The QToothpick 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 Qtoothpicks.
At stage 1 we place two opposite Qtoothpicks centered at (0,0). One of the Qtoothpicks lies on the first quadrant with its endpoints at (0,1) and (1,0). The other Qtoothpick 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 Qtoothpicks, so a(2) = 2+6 = 8.
At stage 3 we place 8 Qtoothpicks, so a(3) = 8+8 = 16.
At stage 4 we place 14 Qtoothpicks, so a(4) = 16+14 = 30.
After 4 stages in the Qtoothpick structure there are 1 circle, 2 "heads" and 12 exposed endpoints.


CROSSREFS

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


KEYWORD

nonn


AUTHOR

Omar E. Pol, Mar 30 2011


EXTENSIONS

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


STATUS

approved



