

A323651


Number of elements added at nth stage to the toothpick structure of A323650.


8



1, 2, 4, 8, 4, 8, 12, 24, 4, 8, 12, 24, 12, 24, 36, 72, 4, 8, 12, 24, 12, 24, 36, 72, 12, 24, 36, 72, 36, 72, 108, 216, 4, 8, 12, 24, 12, 24, 36, 72, 12, 24, 36, 72, 36, 72, 108, 216, 12, 24, 36, 72, 36, 72, 108, 216, 36, 72, 108, 216, 108, 216, 324, 648, 4, 8, 12, 24, 12, 24, 36, 72, 12, 24, 36, 72, 36, 72, 108, 216
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

The oddindexed terms (a bisection) gives A147582, the first differences of A147562 (UlamWarburton cellular automaton).
The evenindexed terms (a bisection) gives A147582 multiplied by 2.
The word of this cellular automaton is "ab", so 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 Itoothpicks. Columns "b" contain numbers of Vtoothpicks. See the example.
For further information about the word of cellular automata see A296612.


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


FORMULA

a(2n1) = A147582(n).
a(2n) = 2*A147582(n).
a(n) = 4*A323641(n2), n >= 3.


EXAMPLE

Written as an irregular triangle the sequence begins:
1,2;
4,8;
4,8,12,24;
4,8,12,24,12,24,36,72;
4,8,12,24,12,24,36,72,12,24,36,72,36,72,108,216;
4,8,12,24,12,24,36,72,12,24,36,72,36,72,108,216,12,24,36,72,36,72,108,216,...
...


CROSSREFS

First differences of A323650.
Cf. A011782, A139250, A139251, A147562, A147582, A160120, A160121, A161206, A161207, A296612, A323641, A323642, A323649.
For other hybrid cellular automata, see A194701, A194271, A220501, A290221, A294021, A294981.
Sequence in context: A191333 A078479 A060968 * A151569 A016635 A133992
Adjacent sequences: A323648 A323649 A323650 * A323652 A323653 A323654


KEYWORD

nonn


AUTHOR

Omar E. Pol, Feb 04 2019


STATUS

approved



