A152978 a(n) = A139251(n+2)/4 = A152968(n+1)/2.

1, 1, 1, 2, 3, 2, 1, 2, 3, 3, 4, 7, 8, 4, 1, 2, 3, 3, 4, 7, 8, 5, 4, 7, 9, 10, 15, 22, 20, 8, 1, 2, 3, 3, 4, 7, 8, 5, 4, 7, 9, 10, 15, 22, 20, 9, 4, 7, 9, 10, 15, 22, 21, 14, 15, 23, 28, 35, 52, 64, 48, 16, 1, 2, 3, 3, 4, 7, 8, 5, 4, 7, 9, 10, 15, 22, 20, 9, 4, 7, 9, 10, 15, 22, 21, 14, 15, 23

Offset: 1

Author

Omar E. Pol, Dec 16 2008, Dec 20 2008

Keywords

• nonn
• easy

Comments

Also, first differences of toothpick numbers A153000.

Examples

			If written as a triangle, begins:
.1,1;
.1,2,3,2;
.1,2,3,3,4,7,8,4;
.1,2,3,3,4,7,8,5,4,7,9,10,15,22,20,8;
....
Rows converge to A152980.
It appears that row sums give A004171. [From _Omar E. Pol_, May 25 2010]
		

Links

• David Applegate, The movie version
• 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. toothpick sequence A139250.

Cf. A139251, A139252, A139560, A152968, A152973.

Cf. A152980, A152998, A153000, A153001, A153003, A153004, A153006.

Cf. A004171. [From Omar E. Pol, May 25 2010]

Formula

G.f.: (1+x)*(Prod(1+x^(2^k-1)+2*x^(2^k),k=1..oo)-1)/(1+2*x). - N. J. A. Sloane, May 20 2009

Extensions

More terms from Omar E. Pol, Jul 26 2009