A182634 Toothpick sequence on hexagonal net starting at the vertex of an infinite 120-degree wedge.

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

Offset: 0

Author

Omar E. Pol, Dec 08 2010

Keywords

• nonn
• more

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.]
• N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS
• Index entries for sequences related to toothpick sequences [From _Omar E. Pol_, Dec 06 2009]
• Index entries for sequences related to cellular automata

Crossrefs

Cf. A139250, A160406, A160120, A161206, A161644, A182632, A182633, A182635.

Formula

a(n) = A182632(n)/3.