A173531 a(0)=0: For n>0, a(n) = A060632(n)*A060632(n-1).

0, 1, 2, 4, 4, 4, 8, 16, 8, 4, 8, 16, 16, 16, 32, 64, 16, 4, 8, 16, 16, 16, 32, 64, 32, 16, 32, 64, 64, 64, 128, 256, 32, 4, 8, 16, 16, 16, 32, 64, 32, 16, 32, 64, 64, 64, 128, 256, 64, 16, 32, 64, 64, 64, 128, 256, 128, 64, 128, 256, 256

Offset

0,3

Comments

First differences of A173530.

Number of triangles (Or V-toothpicks, or L-toothpicks, etc.) added in the three-dimensional structure of A173530 at the n-th stage.

Links

Michael De Vlieger, Table of n, a(n) for n = 0..16383

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.]

Christina Talar Bekaroğlu, Analyzing Dynamics of Larger than Life: Impacts of Rule Parameters on the Evolution of a Bug's Geometry, Master's thesis, Calif. State Univ. Northridge (2023). See p. 92.

Michael De Vlieger, Scatterplot of Log_2 a(n) for n = 1..1024.

N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS

Example

If written as a triangle, begins:
0;
1;
2;
4,4;
4,8,16,8;
4,8,16,16,16,32,64,16;
4,8,16,16,16,32,64,32,16,32,64,64,64,128,256,32;
4,8,16,16,16,32,64,32,16,32,64,64,64,128,256,64,16,32,64,64,64,128,256,128,...

Mathematica

Prepend[Times @@@ Partition[Array[2^DigitCount[Floor[#/2], 2, 1] &, 120, 0], 2, 1], 0] (* Michael De Vlieger, Jan 11 2024 *)

Crossrefs

Cf. A001316, A047999, A060632, A139250, A139251, A161207, A172311, A173530, A173532.

Sequence in context: A182635 A188346 A309690 * A122788 A078003 A081524

Adjacent sequences: A173528 A173529 A173530 * A173532 A173533 A173534

Keyword

nonn

Author

Omar E. Pol, Oct 10 2010

Status

approved