A187221 First differences of A187220.

0, 1, 2, 4, 8, 8, 8, 16, 24, 16, 8, 16, 24, 24, 32, 56, 64, 32, 8, 16, 24, 24, 32, 56, 64, 40, 32, 56, 72, 80, 120, 176, 160, 64, 8, 16, 24, 24, 32, 56, 64, 40, 32, 56, 72, 80, 120, 176, 160, 72, 32, 56, 72, 80, 120, 176, 168, 112, 120, 184, 224, 280, 416, 512, 384, 128, 8

Offset

0,3

Comments

Number of gulls (or G-toothpicks) added at n-th stage to the gullwing structure of A187220.

Apparently this is the connection between A147582 and A139251. - Omar E. Pol, Mar 11 2011

Links

Table of n, a(n) for n=0..66.

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

a(0)=0. a(1)=1. It appears that a(n) = 2*A139251(n-1), for n >= 2.

Example

If written as an irregular triangle begins:
0,
1,
2,
4,
8,8,
8,16,24,16,
8,16,24,24,32,56,64,32,
8,16,24,24,32,56,64,40,32,56,72,80,120,176,160,64,
...
Also there is another version in which the layout of the irregular triangle was adjusted to reveal that the columns become constant:
.0,
.1,
.2,
.4,8,
.8,8,16,24,
16,8,16,24,24,32,56,64,
32,8,16,24,24,32,56,64,40,32,56,72,80,120,176,160,
64,8,16,24,24,32,56,64,40,32,56,72,80,120,176,160,72,32,56,72,80...

Crossrefs

Cf. A139250, A139251, A147582, A187211, A187220.

Sequence in context: A162794 A172305 A366569 * A129280 A103224 A198346

Adjacent sequences: A187218 A187219 A187220 * A187222 A187223 A187224

Keyword

nonn

Author

Omar E. Pol, Mar 07 2011, Mar 09 2011

Status

approved