A266533 -id:A266533 - cp's OEIS frontend

A267701 a(n) = (A160121(n) - A266533(n))/6.

0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 4, 0, 0, 0, 1, 0, 0, 1, 4, 0, 1, 1, 5, 2, 4, 4, 13, 2, 0, 0, 1, 0, 1, 1, 4, 0, 1, 1, 5, 2, 4, 4, 13, 2, 1, 1, 5, 2, 5, 6, 16, 5, 4, 4, 15, 8, 13, 15, 38, 10, 0, 0, 1, 0, 1

Offset: 1

Omar E. Pol, Jan 19 2016

a(n) is 1/6 of the difference between the number of Y-toothpicks added at n-th stage in the structure of A160120 and the number of Y-toothpicks added at n-th stage stage in the structure of A266532 (the outward version of A160120).

			Written as an irregular triangle in which the row lengths are the terms of A011782 the sequence begins:
0;
0;
0,  0;
0,  0,0,0;
1,  0,0,0,1,0,1,1;
4,  0,0,0,1,0,0,1,4,0,1,1,5,2,4,4;
13, 2,0,0,1,0,1,1,4,0,1,1,5,2,4,4,13,2,1,1,5,2,5,6,16,5,4,4,15,8,13,15;
38,10,0,0,1,0,1...

Cf. A011782, A038573, A160120, A160121, A266532, A266533.

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

Original entry on oeis.org

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

David Applegate and Omar E. Pol, Jan 18 2016

nonn

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).

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

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

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

cp's OEIS Frontend

A267701 a(n) = (A160121(n) - A266533(n))/6.

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