The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A160407

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A160407

First differences of toothpick numbers A160406.
(history; published version)

#20 by N. J. A. Sloane at Wed Feb 24 02:48:18 EST 2021

LINKS

David Applegate, Omar E. Pol and N. J. A. Sloane, <a href="http://neilsloane.com/docA000695/tootha000695_1.pdf">The Toothpick Sequence and Other Sequences from Cellular Automata</a>, 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.]

Discussion

Wed Feb 24

02:48

OEIS Server: https://oeis.org/edit/global/2889

#19 by Susanna Cuyler at Sun Apr 19 12:46:37 EDT 2020

STATUS

proposed

approved

#18 by Michel Marcus at Sun Mar 15 15:53:40 EDT 2020

STATUS

editing

proposed

#17 by Michel Marcus at Sun Mar 15 15:53:35 EDT 2020

EXAMPLE

From Omar E. Pol, Jul 18 2009; , Mar 15 2020: (Start)

#16 by Michel Marcus at Sun Mar 15 15:52:40 EDT 2020

EXAMPLE

Contribution from _From _Omar E. Pol_, Jul 18 2009; Mar 15 2020: (Start)

Reformatted by Omar E. Pol, Mar 15 2020

STATUS

proposed

editing

#15 by Omar E. Pol at Sun Mar 15 15:21:20 EDT 2020

STATUS

editing

proposed

#14 by Omar E. Pol at Sun Mar 15 15:21:17 EDT 2020

COMMENTS

This arrangement has the property that the odd-indexed columns (a) contain numbers of the toothpicks that are parallel to initial toothpick, and the even-indexed columns (b) contain numbers of the toothpicks that are orthogonal to the initial toothpick.

#13 by Omar E. Pol at Sun Mar 15 15:18:20 EDT 2020

COMMENTS

The cellular automaton described in A160406 has word "ab", so the structure of the this triangle is as follows:

#12 by Omar E. Pol at Sun Mar 15 15:17:38 EDT 2020

EXAMPLE

Reformatted by _Omar E. Pol, _, Mar 15 2020

#11 by Omar E. Pol at Sun Mar 15 15:16:42 EDT 2020

COMMENTS

From Omar E. Pol, Mar 15 2020: (Start)

The cellular automaton described in A160406 has word "ab", so the structure of the 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;

...

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, ...

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

EXAMPLE

1,1;

1;

Reformatted by _Omar E. Pol, Mar 15 2020

CROSSREFS

Cf. A011782, A139250, A139251, A153000, A153006, A152980, A160406, A161830, A161831, A296612.

STATUS

approved

editing