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A160167 Total number of single toothpicks after n-th stage in the Y-toothpick structure of A160120. 2
0, 3, 12, 21, 48, 57, 84, 111, 174, 201, 228, 255, 318, 363, 426, 507, 660, 741, 768, 795, 858, 903, 966, 1047, 1200, 1299, 1362, 1443, 1596, 1749, 1920, 2127, 2478, 2721, 2784, 2811, 2874, 2919, 2982, 3063, 3216, 3315, 3378, 3459, 3612, 3765, 3936, 4143, 4494, 4755, 4854, 4935 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Also, replace the Y-toothpick with the "three-diamonds" symbol, so we have a new cellular automaton in which a(n) counts the total number of diamonds in the structure after the n-th stage, A160120 also gives the total number of "three-diamonds" symbols after the n-th stage, and A253770 gives the total number of triangular ON cells after the n-th stage. - Omar E. Pol, Feb 10 2015
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.]
FORMULA
a(n) = 3*A160120(n).
a(n) = 3*A160157(n)/2 = A253770(n)/2. - Omar E. Pol, Feb 10 2015
EXAMPLE
From Omar E. Pol, Feb 10 2015: (Start)
After one generation, also, the cellular automaton looks like a star or a flower with three petals as shown below:
.
. /\
. _\/_
. /_/\_\
.
There are six ON cells and three diamonds, so a(1) = 3.
(End)
CROSSREFS
Sequence in context: A119507 A044436 A210282 * A160412 A091846 A061262
KEYWORD
nonn
AUTHOR
Omar E. Pol, Jun 01 2009, Jun 09 2009
EXTENSIONS
New name and more terms from Omar E. Pol, Feb 10 2015
STATUS
approved

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Last modified June 14 08:50 EDT 2024. Contains 373393 sequences. (Running on oeis4.)