The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A182836 Toothpick sequence starting at the vertex of the outside corner of an infinite 120-degree wedge on hexagonal net. 2

%I

%S 0,1,3,7,15,27,39,51,71,91,107

%N Toothpick sequence starting at the vertex of the outside corner of an infinite 120-degree wedge on hexagonal net.

%C Corner sequence for the toothpick structure on hexagonal net.

%C The sequence gives the number of toothpicks after n stages. A182837 (the first differences) gives the number added at the n-th stage. For more information see A182632 and A153006.

%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>

%H <a href="/index/To#toothpick">Index entries for sequences related to toothpick sequences</a>

%e We start at stage 0 with no toothpicks.

%e At stage 1 we place a single toothpick touching a vertex of the infinite hexagon, in direction to the center of the hexagon, but on the outside corner, so a(1)=1.

%e At stage 2 we place 2 toothpicks touching the exposed endpoint of the initial toothpick, so a(2)=1+2=3.

%e At stage 3 we place 4 toothpicks, so a(3)=3+4=7.

%e At stage 4 we place 8 toothpicks, so a(4)=7+8=15.

%e At stage 5 we place 12 toothpicks, so a(5)=15+12=27.

%e After 5 stages the toothpick structure has 5 hexagons and 6 exposed endpoints.

%Y Cf. A139250, A153006, A182632, A182634, A182837, A182840.

%K nonn,more

%O 0,3

%A _Omar E. Pol_, Dec 12 2010

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

Last modified July 31 21:28 EDT 2021. Contains 346377 sequences. (Running on oeis4.)