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A160173 Number of T-toothpicks added at n-th stage to the T-toothpick structure of A160172. 16
0, 1, 3, 5, 9, 9, 9, 13, 25, 21, 9, 13, 25, 25, 25, 37, 73, 57, 9, 13, 25, 25, 25, 37, 73, 61, 25, 37, 73, 73, 73, 109, 217, 165, 9, 13, 25, 25, 25, 37, 73, 61, 25, 37, 73, 73, 73, 109, 217, 169, 25, 37, 73, 73, 73, 109, 217, 181, 73, 109, 217, 217, 217, 325, 649, 489, 9, 13, 25 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
Essentially the first differences of A160172.
For further information see the Applegate-Pol-Sloane paper, chapter 11: T-shaped toothpicks. See also the figure 16 in the mentioned paper. - Omar E. Pol, Nov 18 2011
The numbers n in increasing order such that the triple [n, n, n] can be found here, give A199111. [Observed by Omar E. Pol, Nov 18 2011. Confirmed by Alois P. Heinz, Nov 21 2011]
REFERENCES
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
LINKS
David Applegate, The movie version
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.], which is also available at arXiv:1004.3036v2
FORMULA
a(n) = (2/3)*(3^wt(n-1) + 3^wt(n-2))+1 (where wt is A000120), for n >= 3. - N. J. A. Sloane, Jan 01 2010
EXAMPLE
From Omar E. Pol, Feb 09 2010: (Start)
If written as a triangle:
0;
1;
3;
5;
9,9;
9,13,25,21;
9,13,25,25,25,37,73,57;
9,13,25,25,25,37,73,61,25,37,73,73,73,109,217,165;
9,13,25,25,25,37,73,61,25,37,73,73,73,109,217,169,25,37,73,73,73,109,217,181,73,109,217,217,217,325,649,489;
9,13,25,25,25,37,73,61,25,37,73,73,73,109,217,169,25,37,73,73,73,109...
(End)
MATHEMATICA
wt[n_] := DigitCount[n, 2, 1];
a[0] = 0; a[1] = 1; a[2] = 3; a[n_] := 2/3 (3^wt[n-1] + 3^wt[n-2]) + 1;
Table[a[n], {n, 0, 68}] (* Jean-François Alcover, Aug 18 2018, after N. J. A. Sloane *)
CROSSREFS
Sequence in context: A254689 A176445 A292863 * A256537 A092996 A141264
KEYWORD
nonn
AUTHOR
Omar E. Pol, Jun 01 2009
EXTENSIONS
More terms from N. J. A. Sloane, Jan 01 2010
STATUS
approved

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Last modified July 12 19:17 EDT 2024. Contains 374252 sequences. (Running on oeis4.)