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A168113 First differences of A168112. 3
1, 1, 2, 3, 3, 3, 6, 7, 6, 3, 6, 7, 8, 9, 16, 17, 10, 3, 6, 7, 8, 9, 16, 17, 12, 9, 16, 19, 22, 31, 46, 41, 18, 3, 6, 7, 8, 9, 16, 17, 12, 9, 16, 19, 22, 31, 46, 41, 20, 9, 16, 19, 22, 31, 46, 43, 30, 31, 48 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

a(n) is the number of toothpicks added at the n-th round in the toothpick structure of A168112.

LINKS

Table of n, a(n) for n=1..59.

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.]

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

FORMULA

Observation: It appears that a(2^i+2) = 3, for i>0.

a(n) = A160731(n)/2. [From Nathaniel Johnston, Mar 28 2011]

EXAMPLE

If written as a triangle, begins:

1;

1;

2;

3,3;

3,6,7,6;

3,6,7,8,9,16,17,10;

3,6,7,8,9,16,17,12,9,16,19,22,31,46,41,18;

Rows converge to A168114.

CROSSREFS

Cf. A139250, A139251, A152978, A152980, A160407, A168112, A168114.

Sequence in context: A245642 A289559 A070167 * A170895 A141479 A055081

Adjacent sequences:  A168110 A168111 A168112 * A168114 A168115 A168116

KEYWORD

nonn,tabf

AUTHOR

Omar E. Pol, Dec 07 2009

EXTENSIONS

Terms after a(34) from Nathaniel Johnston, Mar 28 2011

STATUS

approved

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Last modified August 24 18:12 EDT 2019. Contains 326295 sequences. (Running on oeis4.)