%I #6 Feb 24 2021 02:48:18

%S 0,1,3,5,9,11,15,19,27,31,35,39,47,53,61,71,89,99,103

%N Y-toothpick triangle (see Comments lines for definition).

%C Y-toothpick sequence starting at the corner of an infinite hexagon in which its vertex touch an endpoint of the initial Y-toothpick and the two other endpoints are equidistant from the nearest sides of the hexagon.

%C The sequence gives the number of Y-toothpicks in the structure after n rounds. A161831 (the first differences) gives the number added at the n-th round.

%C See the Y-toothpick sequence A160120 for more information about the recursive, fractal-like structure.

%H David Applegate, Omar E. Pol and N. J. A. Sloane, <a href="/A000695/a000695_1.pdf">The Toothpick Sequence and Other Sequences from Cellular Automata</a>, 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.]

%H N. J. A. Sloane, <a href="/wiki/Catalog_of_Toothpick_and_CA_Sequences_in_OEIS">Catalog of Toothpick and Cellular Automata Sequences in the OEIS</a>

%Y Cf. A139250, A160120, A160121, A160406, A160407, A161831, A161832, A161833.

%K more,nonn

%O 0,3

%A _Omar E. Pol_, Jun 20 2009