

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
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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 nth 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), 157191. [There is a typo in Theorem 6: (13) should read u(n) = 4.3^(wt(n1)1) for n >= 2.]
John W. Layman, Graphs of the toothpick configuration for generations 115
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*(n2 + Sum_{k=1..n2}3^A000120(k)), n >= 2.
a(n) = 7 + 4*(n2 + 3*A151920(n3)), 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



