A194435 Number of toothpicks or D-toothpicks added at n-th stage to the structure of A194434.

0, 4, 8, 16, 16, 16, 32, 44, 32, 16, 32, 64, 96, 48, 80, 100, 64, 16, 32, 64, 96, 112, 144, 168, 176, 80, 96, 160, 256, 128, 176, 212, 128, 16, 32, 64, 96, 112, 144, 176, 208, 168, 192, 240, 400, 272, 336, 332, 336, 112, 96, 176, 288, 336, 416, 464

Offset

0,2

Comments

Essentially the first differences of A194434.

First differs from A221528 at a(13). - Omar E. Pol, Mar 23 2013

From Omar E. Pol, Jun 24 2022: (Start)

The word of this cellular automaton is "ab".

For the nonzero terms the structure of the irregular triangle is as shown below:

a,b;

a,b;

a,b,a,b;

a,b,a,b,a,b,a,b;

a,b,a,b,a,b,a,b,a,b,a,b,a,b,a,b;

...

Row lengths are the terms of A011782 multiplied by 2, also the column 2 of A296612.

Columns "a" contain numbers of D-toothpicks (of length sqrt(2)).

Columns "b" contain numbers of toothpicks (of length 1).

An associated sound to the animation could be (tick, tock), (tick, tock), ..., the same as the ticking clock sound.

For further information about the word of cellular automata see A296612. (End)

Links

Table of n, a(n) for n=0..55.

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

Paolo Xausa, Animated version for n = 0..31 (red elements)

Paolo Xausa, Animated version for n = 0..63 (red elements)

Paolo Xausa, Illustration of initial terms for n = 0..63 (red elements, multipage PDF)

Index entries for sequences related to toothpick sequences

Formula

a(n) = 4*A194445(n).

Conjecture: a(2^k+1) = 16, if k >= 1.

Example

From Omar E. Pol, Mar 23 2013: (Start)
When written as an irregular triangle the sequence of nonzeros terms begins:
   4, 8;
  16,16;
  16,32,44,32;
  16,32,64,96, 48, 80,100, 64;
  16,32,64,96,112,144,168,176, 80, 96,160,256,128,176,212,128;
  16,32,64,96,112,144,176,208,168,192,240,400,272,336,332,336,112,96, ...
  ... (End)
Right border gives the powers of 2 >= 8 (reformatted the triangle). - Omar E. Pol, Jun 24 2022

Crossrefs

Cf. A011782, A139251, A194271, A194433, A194434, A194441, A194443, A194445, A212009, A221528, A299612.

Sequence in context: A045534 A194433 A221565 * A221528 A312759 A312760

Adjacent sequences: A194432 A194433 A194434 * A194436 A194437 A194438

Keyword

nonn,tabf

Author

Omar E. Pol, Sep 03 2011

Extensions

More terms from Omar E. Pol, Mar 23 2013

Status

approved