A220521 Number of toothpicks or D-toothpicks added at n-th stage in the toothpick structure of A220520.

1, 2, 4, 4, 4, 4, 8, 8, 4, 4, 8, 12, 16, 12, 16, 16, 4, 4, 8, 12, 16, 20, 24, 26, 24, 12, 20, 32, 40, 28, 32, 32, 4, 4, 8, 12, 16, 20, 24, 26, 24, 20, 32, 44, 64, 52, 48, 54, 40, 12, 20, 36, 48, 56, 64, 74, 76, 30, 44, 72, 88, 60, 64, 64, 4, 4, 8, 12

Offset

1,2

Comments

From Omar E. Pol, Apr 26 2020: (Start)

The cellular automaton described in A220520 has word "ab", so the structure of this triangle is as follows:

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;

...

The row lengths are the terms of A011782 multiplied by 2, equaling the column 2 of the square array A296612: 2, 2, 4, 8, 16, ...

This arrangement has the property that the odd-indexed columns (a) contain numbers of the toothpicks of length 1, and the even-indexed columns (b) contain numbers of the D-toothpicks.

For further information about the "word" of a cellular automaton see A296612. (End)

Links

Table of n, a(n) for n=1..68.

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

Index entries for sequences related to toothpick sequences

Example

Written as an irregular triangle the sequence begins:
1,2;
4,4;
4,4,8,8;
4,4,8,12,16,12,16,16;
4,4,8,12,16,20,24,26,24,12,20,32,40,28,32,32;
4,4,8,12,16,20,24,26,24,20,32,44,64,52,48,54,40,12,20,...
Triangle reformatted by Omar E. Pol, Apr 26 2020

Crossrefs

First differences of A220520.

First differs from A194441 at a(14).

Columns 1-3: A123932, A040002, A010731.

Cf. A139250, A139251, A194443, A220501, A220523, A296612.

Sequence in context: A235863 A220495 A194441 * A236680 A162798 A088650

Adjacent sequences: A220518 A220519 A220520 * A220522 A220523 A220524

Keyword

nonn,tabf

Author

Omar E. Pol, Dec 15 2012

Extensions

0 removed and offset changed by Omar E. Pol, Apr 26 2020

Status

approved