A160173 -id:A160173 - cp's OEIS frontend

A160714 T-toothpick sequence starting at the corner of an infinite square, but with angle = Pi/4.

Original entry on oeis.org

0, 1, 2, 5, 6, 9, 12, 21, 22, 25, 28, 37, 40, 49, 58, 85, 112, 113

Offset: 0

Omar E. Pol, Jun 02 2009

The sequence gives the number of T-toothpicks after n rounds.

See A160172 for more information about T-toothpick sequences.

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, A160172, A160173.

A160724 a(n) = A160714(n)*3.

Original entry on oeis.org

0, 3, 6, 15, 18, 27, 36, 63, 66, 75, 84, 111, 120, 147, 174, 255, 336, 339

Offset: 0

Omar E. Pol, Jun 02 2009

The sequence gives the number of T-toothpicks in the structure after n rounds.

See A160172 and A160714 for more information about T-toothpick sequences.

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, A160172, A160173, A160714, A160726.

a(9)-a(17) from 3*A160714(n) by Jinyuan Wang, Mar 14 2020

A160726 a(n) = A160714(n)*4.

Original entry on oeis.org

0, 4, 8, 20, 24, 36, 48, 84, 88, 100, 112, 148, 160, 196, 232, 340, 448, 452

Offset: 0

Omar E. Pol, Jun 02 2009

The sequence gives the number of T-toothpicks in the structure after n rounds.

See A160172 and A160714 for more information about T-toothpick sequences.

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, A160172, A160173, A160714, A160716, A160724.

a(9)-a(17) from 4*A160714(n) by Jinyuan Wang, Mar 14 2020

A183127 Number of toothpicks added at n-th stage to the toothpick structure of A183126.

Original entry on oeis.org

0, 1, 6, 16, 16, 40, 16, 40, 40, 112, 16, 40, 40, 112, 40, 112, 112, 328, 16, 40, 40, 112, 40, 112, 112, 328, 40, 112, 112, 328, 112, 328, 328, 976, 16, 40, 40, 112, 40, 112, 112, 328, 40, 112, 112, 328, 112, 328, 328, 976, 40, 112, 112, 328, 112, 328, 328, 976

Offset: 0

Omar E. Pol, Mar 28 2011

nonn

Essentially the first differences of A183126.

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. A000120, A139250, A139251, A160173, A161411, A183126, A183149.

a[n_] := 4*(1 + 3^DigitCount[n-2, 2, 1]); a[0] = 0; a[1] = 1; a[2] = 6; Array[a, 100, 0] (* Amiram Eldar, Aug 01 2023 *)

a(n) = 4*(1 + 3^A000120(n-2)), n >= 3. - Nathaniel Johnston, Apr 06 2011

a(0)-a(10) confirmed and a(11)-a(35) added by John W. Layman, Mar 30 2011
a(36)-a(47) from Nathaniel Johnston, Apr 06 2011
More terms from Amiram Eldar, Aug 01 2023

A183149 Number of toothpicks added at n-th stage to the toothpick structure of A183148.

Original entry on oeis.org

0, 1, 3, 9, 9, 21, 9, 21, 21, 57, 9, 21, 21, 57, 21, 57, 57, 165, 9, 21, 21, 57, 21, 57, 57, 165, 21, 57, 57, 165, 57, 165, 165, 489, 9, 21, 21, 57, 21, 57, 57, 165, 21, 57, 57, 165, 57, 165, 165, 489, 21, 57, 57, 165, 57, 165

Offset: 0

Omar E. Pol, Mar 28 2011, Apr 02 2011

nonn

Essentially the first differences of A183148.

			If written as a triangle begins:
0,
1,
3,
9,
9,21,
9,21,21,57,
9,21,21,57,21,57,57,165,
9,21,21,57,21,57,57,165,21,57,57,165,57,165,165,489,

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, A147582, A147610, A160173, A161411, A183061, A183127, A183148.

a(n) = 3*A183061(n-1), for n >=2

A160716 a(n) = A160714(n)*2.

Original entry on oeis.org

0, 2, 4, 10, 12, 18, 24, 42, 44, 50, 56, 74, 80, 98, 116, 170, 224, 226

Offset: 0

Omar E. Pol, Jun 02 2009

The sequence gives the number of T-toothpicks in the structure after n rounds.

See A160172 and A160714 for more information about T-toothpick sequences.

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, A160172, A160173, A160714, A160724, A160726.

cp's OEIS Frontend

A160714 T-toothpick sequence starting at the corner of an infinite square, but with angle = Pi/4.

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A160724 a(n) = A160714(n)*3.

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A160726 a(n) = A160714(n)*4.

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A183127 Number of toothpicks added at n-th stage to the toothpick structure of A183126.

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A183149 Number of toothpicks added at n-th stage to the toothpick structure of A183148.

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A160716 a(n) = A160714(n)*2.

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