login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Today, Nov 11 2014, is the 4th anniversary of the launch of the new OEIS web site. 70,000 sequences have been added in these four years, all edited by volunteers. Please make a donation (tax deductible in the US) to help keep the OEIS running.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified December 18 21:27 EST 2014. Contains 252174 sequences.