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

Author

Omar E. Pol, Dec 07 2009

Keywords

• nonn
• tabf

Comments

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

Examples

			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.
		

Links

• 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

Crossrefs

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

Formula

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

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

Extensions

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