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

Author

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

Keywords

• nonn
• tabf

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)

Examples

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

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]

Crossrefs

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

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

Programs

Mathematica

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

Formula

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

Extensions

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