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A182836 Toothpick sequence starting at the vertex of the outside corner of an infinite 120-degree wedge on hexagonal net. 2
0, 1, 3, 7, 15, 27, 39, 51, 71, 91, 107 (list; graph; refs; listen; history; text; internal format)



Corner sequence for the toothpick structure on hexagonal net.

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.


Table of n, a(n) for n=0..10.

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.]

N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS

Index entries for sequences related to toothpick sequences


We start at stage 0 with no toothpicks.

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.

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

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

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

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

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


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

Sequence in context: A213215 A324719 A170884 * A097080 A274008 A146742

Adjacent sequences:  A182833 A182834 A182835 * A182837 A182838 A182839




Omar E. Pol, Dec 12 2010



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Last modified June 14 08:31 EDT 2021. Contains 345018 sequences. (Running on oeis4.)