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A183126 Toothpick sequence with toothpicks connected by their endpoints. 3
0, 1, 7, 23, 39, 79, 95, 135, 175, 287, 303, 343, 383, 495, 535, 647, 759, 1087, 1103, 1143, 1183, 1295, 1335, 1447, 1559, 1887, 1927, 2039, 2151, 2479, 2591, 2919, 3247, 4223, 4239, 4279, 4319, 4431, 4471, 4583, 4695 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

On the infinite square grid we start with no toothpicks.

At stage 1 we place a single toothpick of length 1.

Rule: each exposed endpoint of the toothpicks of the old generation must be touched by the endpoints of three toothpicks of new generation.

The sequence gives the number of toothpicks after n stages. A183127 gives the number of toothpicks added at the n-th stage.

LINKS

Table of n, a(n) for n=0..40.

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. [There is a typo in Theorem 6: (13) should read u(n) = 4.3^(wt(n-1)-1) for n >= 2.]

John W. Layman, Graphs of the toothpick configuration for generations 1-15

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

FORMULA

From Nathaniel Johnston, Apr 06 2011: (Start)

a(n) = 7 + 4*(n-2 + Sum_{k=1..n-2}3^A000120(k)), n >= 2.

a(n) = 7 + 4*(n-2 + 3*A151920(n-3)), n >= 3.

a(1 + 2^n) = 2^(n+2)+4^(n+1)-1, n >= 0.

(End)

CROSSREFS

Cf. A139250, A160172, A160410, A183004, A183127, A183148.

Sequence in context: A227064 A143030 A031043 * A213632 A031095 A319050

Adjacent sequences:  A183123 A183124 A183125 * A183127 A183128 A183129

KEYWORD

nonn

AUTHOR

Omar E. Pol, Mar 28 2011

EXTENSIONS

Terms a(0)-a(10) confirmed and terms a(11)-a(35) added by John W. Layman, Mar 30 2011

a(36)-a(40) from Nathaniel Johnston, Apr 06 2011

STATUS

approved

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Last modified August 5 08:27 EDT 2021. Contains 346464 sequences. (Running on oeis4.)