A162795 -id:A162795 - cp's OEIS frontend

A173464 When regarded as a triangle, the rows of A162797 converge to this sequence.

1, 5, 5, 17, 5, 17, 21, 49, 5, 17, 21, 49, 21, 53, 81, 129, 5, 17, 21, 49, 21, 53, 81, 129, 21, 53, 81, 133, 81, 165, 289, 321

Offset: 1

Omar E. Pol, Feb 22 2010

			From _Omar E. Pol_, Apr 01 2011: (Start)
If written as a triangle begins:
1,
5,
5,17,
5,17,21,49,
5,17,21,49,21,53,81,129,
5,17,21,49,21,53,81,129,21,53,81,133,81,165,289,321,
...
It appears that the final terms of rows give A000337.
It appears that row sums give A010036.
(End)

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

Cf. A139250, A162795, A162796, A162797.

Cf. A010036, A162793, A162794. - Omar E. Pol, Apr 01 2011

More terms a(20)-a(32) from Omar E. Pol, Apr 01 2011

A163094 a(n) = A162796(n)/2.

Original entry on oeis.org

0, 1, 3, 7, 11, 15, 21, 35, 43, 47, 53, 67, 77, 91, 111, 155, 171, 175, 181, 195, 205, 219, 239, 283, 301, 315, 335, 379, 407, 453, 523, 651, 683, 687, 693, 707, 717, 731, 751, 795, 813, 827, 847, 891, 919, 965, 1035, 1163, 1197, 1211, 1231, 1275, 1303, 1349, 1419

Offset: 0

Omar E. Pol, Jul 28 2009

nonn

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

Cf. A139250, A139251, A159791, A159792, A162793, A162794, A162795, A162796, A162797.

a(0) prepended by and more terms from Jinyuan Wang, Mar 15 2020

A288775 Difference between the total number of toothpicks in the toothpick structure of A139250 that are parallel to the initial toothpick after n odd stages, and the total number of "ON" cells at n-th stage in the "Ulam-Warburton" two-dimensional cellular automaton of A147562.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 4, 4, 28, 0, 0, 0, 4, 0, 4, 4, 28, 0, 4, 4, 28, 4, 28, 32, 132, 0, 0, 0, 4, 0, 4, 4, 28, 0, 4, 4, 28, 4, 28, 32, 132, 0, 4, 4, 28, 4, 28, 32, 132, 4, 28, 32, 132, 32, 136, 176, 524, 0, 0, 0, 4, 0, 4, 4, 28, 0, 4, 4, 28, 4, 28, 32, 132, 0, 4, 4, 28, 4, 28, 32, 132, 4, 28, 32

Offset: 1

Omar E. Pol, Jul 04 2017

It appears that a(n) = 0 if and only if n is a member of A048645.
First differs from A255263 at a(14), with which it shares infinitely many terms.
It appears that A147562(n) = A162795(n) = A169707(n) = A255366(n) = A256250(n) = A256260(n), if n is a member of A048645.

			Written as an irregular triangle T(j,k), k>=1, in which the row lengths are the terms of A011782, the sequence begins:
0;
0;
0,0;
0,0,4,0;
0,0,4,0,4,4,28,0;
0,0,4,0,4,4,28,0,4,4,28,4,28,32,132,0;
0,0,4,0,4,4,28,0,4,4,28,4,28,32,132,0,4,4,28,4,28,32,132,4,28,32,132,32,136,176,524,0;
...
It appears that if k is a power of 2 then T(j,k) = 0.
It appears that every column lists the same terms as its initial term.

Cf. A011782, A048645, A139250, A139251, A147562, A147582, A162793, A162795, A169707, A255263, A255366, A256250, A256260.

a(n) = A162795(n) - A147562(n).

cp's OEIS Frontend

A173464 When regarded as a triangle, the rows of A162797 converge to this sequence.

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A163094 a(n) = A162796(n)/2.

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A288775 Difference between the total number of toothpicks in the toothpick structure of A139250 that are parallel to the initial toothpick after n odd stages, and the total number of "ON" cells at n-th stage in the "Ulam-Warburton" two-dimensional cellular automaton of A147562.

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