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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)
 OFFSET 0,3 COMMENTS 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. 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 EXAMPLE 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. CROSSREFS Cf. A139250, A153006, A182632, A182634, A182837, A182840. Sequence in context: A213215 A324719 A170884 * A097080 A274008 A146742 Adjacent sequences:  A182833 A182834 A182835 * A182837 A182838 A182839 KEYWORD nonn,more AUTHOR Omar E. Pol, Dec 12 2010 STATUS approved

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