A161411 First differences of A160410.

4, 12, 12, 36, 12, 36, 36, 108, 12, 36, 36, 108, 36, 108, 108, 324, 12, 36, 36, 108, 36, 108, 108, 324, 36, 108, 108, 324, 108, 324, 324, 972, 12, 36, 36, 108, 36, 108, 108, 324, 36, 108, 108, 324, 108, 324, 324, 972, 36, 108, 108, 324, 108, 324, 324, 972, 108, 324, 324

Offset

1,1

Comments

The rows of the triangle in A147582 converge to this sequence.

Contribution from Omar E. Pol, Mar 28 2011 (Start):

a(n) is the number of cells turned "ON" at n-th stage of the cellular automaton of A160410.

a(n) is also the number of toothpicks added at n-th stage to the toothpick structure of A160410.

(End)

Links

Paolo Xausa, Table of n, a(n) for n = 1..10000

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

Omar E. Pol, Illustration of initial terms (Neighbors of the vertices) [From Omar E. Pol, Nov 17 2009]

Formula

a(n) = A048883(n-1)*4.

Example

If written as a triangle:
.4;
.12;
.12,36;
.12,36,36,108;
.12,36,36,108,36,108,108,324;

Mathematica

4*3^DigitCount[Range[0, 100], 2, 1] (* Paolo Xausa, Sep 01 2023 *)

Crossrefs

Cf. A139250, A139251, A160413, A160415, A160417.

Cf. A000079, A048883, A147582, A160410, A160414.

Sequence in context: A272841 A272942 A272923 * A261695 A209047 A209019

Adjacent sequences: A161408 A161409 A161410 * A161412 A161413 A161414

Keyword

nonn,tabf

Author

Omar E. Pol, May 20 2009, Jun 13 2009, Jun 14 2009

Extensions

Edited by David Applegate and N. J. A. Sloane, Jul 13 2009

Status

approved