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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 Table of n, a(n) for n=0..51. 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 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 Cf. A139250, A160120, A160157, A253770. Sequence in context: A119507 A044436 A210282 * A160412 A091846 A061262 Adjacent sequences: A160164 A160165 A160166 * A160168 A160169 A160170 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.)