A323647 Number of elements added at n-th stage to the toothpick structure of A323646.

1, 2, 2, 4, 6, 6, 6, 12, 14, 12, 6, 12, 14, 16, 18, 32, 34, 20, 6, 12, 14, 16, 18, 32, 34, 24, 18, 32, 38, 44, 62, 92, 82, 36, 6, 12, 14, 16, 18, 32, 34, 24, 18, 32, 38, 44, 62, 92, 82, 40, 18, 32, 38, 44, 62, 92, 86, 60, 62, 96, 114, 144, 210, 260, 194, 68, 6, 12, 14, 16, 18, 32, 34, 24, 18, 32, 38, 44, 62, 92

Offset

1,2

Comments

The "word" of this cellular automaton is "ab", but note that this triangle has an unusual structure: an additional row of length 2. For more information about the word of cellular automata see A296612.

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,a,b;

...

Row lengths give 2 together with the terms of A011782 multiplied by 2, also 2 togheter with the column 2 of A296612.

Columns "a" contain numbers of toothpicks of length 2.

Columns "b" contain numbers of D-toothpicks of length 2*sqrt(2). See the example.

Links

Table of n, a(n) for n=1..80.

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

Index entries for sequences related to cellular automata

Index entries for sequences related to toothpick sequences

Example

Triangle begins:
1, 2;
2, 4;
6, 6;
6,12,14,12;
6,12,14,16,18,32,34,20;
6,12,14,16,18,32,34,24,18,32,38,44,62,92,82,36;
6,12,14,16,18,32,34,24,18,32,38,44,62,92,82,40,18,32,38,44,62,92,86,60,62,96, ...

Crossrefs

First differences of A323646.

Also, 1 together with A160731.

Column 1 gives A134201.

Cf. A011782, A139251, A296612.

For other hybrid cellular automata, see A194271, A194701, A220501, A289841, A290221, A294021, A294963, A294981, A299771, A323651, A327331, A327333.

Sequence in context: A338276 A062722 A160731 * A302928 A098214 A178883

Adjacent sequences: A323644 A323645 A323646 * A323648 A323649 A323650

Keyword

nonn,tabf

Author

Omar E. Pol, Mar 07 2019

Status

approved