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A183148 Toothpick sequence on the semi-infinite 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

On the semi-infinite 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 T-toothpick (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 n-th stage. The first differences (A183149) give the number of toothpicks added at n-th 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), 157-191

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

FORMULA

a(n) = 3*A183060(n-1) + 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 A063631 A031240

Adjacent sequences:  A183145 A183146 A183147 * A183149 A183150 A183151

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified October 1 22:19 EDT 2014. Contains 247522 sequences.