A266532 Total number of Y-toothpicks after n-th stage in the "outward" version of the cellular automaton of A160120.

0, 1, 4, 7, 16, 19, 28, 37, 58, 61, 70, 79, 100, 109, 130, 151, 196, 199, 208, 217, 238, 247, 268, 289, 334, 343, 364, 385, 430, 451, 496, 541, 634, 637, 646, 655, 676, 685, 706, 727, 772, 781, 802, 823, 868, 889, 934, 979, 1072, 1081, 1102, 1123, 1168, 1189, 1234, 1279, 1372, 1393, 1438, 1483, 1576, 1621, 1714, 1807, 1996, 1999, 2008, 2017

Offset: 0

Author

David Applegate and Omar E. Pol, Jan 18 2016

Keywords

• nonn

Comments

For the connection with A160720 (the "outward" version of the Ulam-Warburton cellular automaton A147562) see formula section and A267700.

A266533 (the first differences) gives the number of Y-toothpicks added to the structure at n-th stage.

First differs from A160120 at a(9).

First differs from A160715 at a(13).

Links

• David Applegate, The movie version
• N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS
• Index entries for sequences related to cellular automata
• Index entries for sequences related to toothpick sequences

Crossrefs

Cf. A139250, A147562, A159912, A160120, A160715, A160720, A266533, A267700, A267701.

Formula

Conjecture: a(n) = 1 + 3*(A160720(n) - 1)/4 = 1 + 3*A267700(n-1), n >= 1. This formula is correct! - N. J. A. Sloane, Jan 23 2016

a(n) = 1 + 3*(A159912(n) - n)/2, n >= 1. - Omar E. Pol, Jan 24 2016