A161910 - OEIS

%I #10 Jun 14 2022 14:12:05

%S 0,1,2,5,6,9,12,19,22,25,28,35,40,47,56,73

%N Y-toothpick sequence starting at the corner of an infinite hexagon from which protrudes a half toothpick with an angle = Pi/6.

%C The sequence gives the number of Y-toothpicks in the structure after n rounds. A160123 (the first differences) gives the number added at the n-th round.

%C See the entries A160120, A161830 and A161426 for more information about Y-toothpick sequences.

%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>

%F a(n) = (A160120(n+1)-1)/3.

%Y Cf. A160120, A160121, A160123, A160406, A161426, A161830, A161831.

%K more,nonn

%O 0,3

%A _Omar E. Pol_, Jun 21 2009