login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A323651 Number of elements added at n-th stage to the toothpick structure of A323650. 8

%I #28 Apr 11 2019 22:49:20

%S 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,

%T 36,72,36,72,108,216,4,8,12,24,12,24,36,72,12,24,36,72,36,72,108,216,

%U 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

%N Number of elements added at n-th stage to the toothpick structure of A323650.

%C The odd-indexed terms (a bisection) gives A147582, the first differences of A147562 (Ulam-Warburton cellular automaton).

%C The even-indexed terms (a bisection) gives A147582 multiplied by 2.

%C The word of this cellular automaton is "ab", so the structure of the irregular triangle is as shown below:

%C a,b;

%C a,b;

%C a,b,a,b;

%C a,b,a,b,a,b,a,b;

%C a,b,a,b,a,b,a,b,a,b,a,b,a,b,a,b;

%C ...

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

%C Columns "a" contain numbers of I-toothpicks. Columns "b" contain numbers of V-toothpicks. See the example.

%C For further information about the word of cellular automata see A296612.

%H N. J. A. Sloane, <a href="/wiki/Catalog_of_Toothpick_and_CA_Sequences_in_OEIS">Catalog of Toothpick and Cellular Automata Sequences in the OEIS</a>

%H <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>

%H <a href="/index/To#toothpick">Index entries for sequences related to toothpick sequences</a>

%F a(2n-1) = A147582(n).

%F a(2n) = 2*A147582(n).

%F a(n) = 4*A323641(n-2), n >= 3.

%e Written as an irregular triangle the sequence begins:

%e 1,2;

%e 4,8;

%e 4,8,12,24;

%e 4,8,12,24,12,24,36,72;

%e 4,8,12,24,12,24,36,72,12,24,36,72,36,72,108,216;

%e 4,8,12,24,12,24,36,72,12,24,36,72,36,72,108,216,12,24,36,72,36,72,108,216,...

%e ...

%Y First differences of A323650.

%Y Cf. A011782, A139250, A139251, A147562, A147582, A160120, A160121, A161206, A161207, A296612, A323641, A323642, A323649.

%Y For other hybrid cellular automata, see A194701, A194271, A220501, A290221, A294021, A294981.

%K nonn

%O 1,2

%A _Omar E. Pol_, Feb 04 2019

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)