

A160173


Number of Ttoothpicks added at nth stage to the Ttoothpick structure of A160172.


14



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
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OFFSET

0,3


COMMENTS

Essentially the first differences of A160172.
For further information see the ApplegatePolSloane paper, chapter 11: Tshaped 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), 157191


LINKS

Table of n, a(n) for n=0..68.
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), 157191. [There is a typo in Theorem 6: (13) should read u(n) = 4.3^(wt(n1)1) for n >= 2.], which is also available at arXiv:1004.3036v2
N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS
Index entries for sequences related to toothpick sequences


FORMULA

a(n) = (2/3)*(3^wt(n1) + 3^wt(n2))+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[n1] + 3^wt[n2]) + 1;
Table[a[n], {n, 0, 68}] (* JeanFrançois Alcover, Aug 18 2018, after N. J. A. Sloane *)


CROSSREFS

Cf. A139250, A139251, A160172, A160121, A160171, A161207, A161329, A172311.
Sequence in context: A254689 A176445 A292863 * A256537 A092996 A141264
Adjacent sequences: A160170 A160171 A160172 * A160174 A160175 A160176


KEYWORD

nonn,changed


AUTHOR

Omar E. Pol, Jun 01 2009


EXTENSIONS

More terms from N. J. A. Sloane, Jan 01 2010


STATUS

approved



