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A182634 Toothpick sequence on hexagonal net starting at the vertex of an infinite 120-degree wedge. 8
0, 1, 3, 7, 11, 15, 23, 35, 43, 47, 55, 71, 91, 107, 127, 155, 171, 175, 183, 199, 219, 239, 267, 311, 355, 379, 399, 439, 495, 543, 595, 659, 691, 695, 703, 719, 739, 759, 787, 831, 875, 903, 931, 983, 1059, 1135, 1211 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
The sequence gives the number of toothpicks after n stages. A182635 (the first differences) gives the number added at the n-th stage.
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.
Toothpicks are connected by their endpoints, the same as the toothpicks of A182632.
First differs from A139250 at a(11).
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.]
FORMULA
a(n) = A182632(n)/3.
CROSSREFS
Sequence in context: A139250 A256265 A266535 * A365142 A173530 A192114
KEYWORD
nonn,more
AUTHOR
Omar E. Pol, Dec 08 2010
STATUS
approved

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Last modified May 28 00:20 EDT 2024. Contains 372900 sequences. (Running on oeis4.)