A182836 Toothpick sequence starting at the vertex of the outside corner of an infinite 120-degree wedge on hexagonal net.
0, 1, 3, 7, 15, 27, 39, 51, 71, 91, 107
Offset: 0
Examples
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.
Links
- 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
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