The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 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), 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 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(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 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 AUTHOR Omar E. Pol, Jun 01 2009 EXTENSIONS More terms from N. J. A. Sloane, Jan 01 2010 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

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