OFFSET
0,3
COMMENTS
From Omar E. Pol, Feb 06 2023: (Start)
The "word" of this cellular automaton is "ab".
Apart from the initial zero 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;
...
Columns "a" contain numbers of toothpicks and D-toothpicks when in the top border of the structure there are only toothpicks (of length 1).
Columns "b" contain numbers of toothpicks and D-toothpicks when in the top border of the structure there are only D-toothpicks (of length sqrt(2)).
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.
It appears that the right border of the irregular triangle gives the even powers of 2. (End)
LINKS
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.]
N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS
FORMULA
EXAMPLE
From Omar E. Pol, Feb 06 2023: (Start)
The nonzero terms can write as an irregular triangle as shown below:
1, 2;
4, 4;
4, 6, 10, 8;
4, 6, 12, 16, 14, 14, 22, 16;
4, 6, 12, 16, 16, 20, 32, 36, 22, 14, 28, 42, 40, 36, 50, 32;
...
(End)
CROSSREFS
KEYWORD
nonn,tabf,more
AUTHOR
Omar E. Pol, Dec 12 2010
EXTENSIONS
a(19)-a(41) from Omar E. Pol, Jan 06 2023
STATUS
approved