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A182634 Toothpick sequence on hexagonal net starting at the vertex of an infinite 120-degree wedge.

%I A182634 #27 Oct 10 2022 10:36:47
%S A182634 0,1,3,7,11,15,23,35,43,47,55,71,91,107,127,155,171,175,183,199,219,
%T A182634 239,267,311,355,379,399,439,495,543,595,659,691,695,703,719,739,759,
%U A182634 787,831,875,903,931,983,1059,1135,1211
%N A182634 Toothpick sequence on hexagonal net starting at the vertex of an infinite 120-degree wedge.
%C A182634 The sequence gives the number of toothpicks after n stages. A182635 (the first differences) gives the number added at the n-th stage.
%C A182634 The 120-degree wedge defines a conic region which toothpicks (except one end point of the initial toothpick) are not allowed to cross or touch. The wings of the wedge point +-60 degrees away from the pointing direction of the initial toothpick.
%C A182634 Toothpicks are connected by their endpoints, the same as the toothpicks of A182632.
%C A182634 First differs from A139250 at a(11).
%H A182634 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 A182634 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>
%H A182634 <a href="/index/To#toothpick">Index entries for sequences related to toothpick sequences</a> [From _Omar E. Pol_, Dec 06 2009]
%H A182634 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%F A182634 a(n) = A182632(n)/3.
%Y A182634 Cf. A139250, A160406, A160120, A161206, A161644, A182632, A182633, A182635.
%K A182634 nonn,more
%O A182634 0,3
%A A182634 _Omar E. Pol_, Dec 08 2010