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

1,4

Comments

Also, first differences of toothpick numbers A153000.

Links

Table of n, a(n) for n=1..88.

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

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

Example

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]

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]

Sequence in context: A030314 A269624 A098236 * A118121 A006968 A058207

Adjacent sequences: A152975 A152976 A152977 * A152979 A152980 A152981

Keyword

nonn,easy

Author

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

Extensions

More terms from Omar E. Pol, Jul 26 2009

Status

approved