A168113 First differences of A168112.

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

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