

A183148


Toothpick sequence on the semiinfinite square grid with toothpicks connected by their endpoints.


2



0, 1, 4, 13, 22, 43, 52, 73, 94, 151, 160, 181, 202, 259, 280, 337, 394, 559, 568, 589, 610, 667, 688, 745, 802, 967, 988, 1045, 1102, 1267, 1324, 1489, 1654, 2143, 2152, 2173, 2194, 2251, 2272, 2329, 2386, 2551, 2572, 2629
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OFFSET

0,3


COMMENTS

On the semiinfinite square grid we start with no toothpicks.
At stage 1 we place a single toothpick of length 1 which has one of its endpoints on the straight line.
New generations of toothpicks are added according to these rules: each exposed endpoint of toothpicks of the old generation must be touched by the 3 endpoints of three toothpicks of the new generation. Effectively these three toothpicks look like a Ttoothpick (see A160172). The straight line that delimits the square grid acts like an impenetrable "absorbing" boundary: toothpicks may touch this line with at most one of their endpoints; these endpoints are not "exposed."
The sequence counts the number of toothpicks in the toothpick structure after nth stage. The first differences (A183149) give the number of toothpicks added at nth stage.


LINKS

Table of n, a(n) for n=0..43.
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
N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS


FORMULA

a(n) = 3*A183060(n1) + 1.


EXAMPLE

At stage 1 place an orthogonal toothpick with one of its endpoints on the infinite straight line, so a(1) = 1. There is only one exposed endpoint.
At stage 2 place 3 toothpicks such that the structure looks like a cross, so a(2) = 1+3 = 4. There are 3 exposed endpoints.
At stage 3 place 9 toothpicks, so a(3) = 4+9 = 13. There are 3 exposed endpoints.
At stage 4 place 9 toothpicks, so a(4) = 13+9 = 22. There are 7 exposed endpoints.


CROSSREFS

Cf. A139250, A147562, A151920, A183004, A183060, A183126, A183149.
Sequence in context: A067396 A017209 A052218 * A202089 A256390 A264623
Adjacent sequences: A183145 A183146 A183147 * A183149 A183150 A183151


KEYWORD

nonn


AUTHOR

Omar E. Pol, Mar 28 2011, Apr 03 2011


STATUS

approved



