A160720 -id:A160720 - cp's OEIS frontend

A160744 a(n) = A151566(n)*3.

0, 3, 6, 12, 18, 24, 30, 42, 54, 60, 66, 78, 90, 102, 114, 138, 162, 168, 174, 186, 198, 210, 222, 246, 270, 282, 294, 318, 342, 366, 390, 438, 486, 492, 498, 510, 522, 534, 546, 570, 594, 606, 618, 642, 666, 690, 714, 762, 810, 822, 834, 858, 882, 906, 930

Offset: 0

Omar E. Pol, May 25 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, A151566, A160720, A160722, A160736, A160738, A160740, A160742, A160746.

More terms from R. J. Mathar, Jul 28 2009

A160723 First differences of A160722.

Original entry on oeis.org

1, 4, 4, 10, 4, 10, 10, 22, 4, 10, 10, 22, 10, 22, 22, 46, 4, 10, 10, 22, 10, 22, 22, 46, 10, 22, 22, 46, 22, 46, 46, 94, 4, 10, 10, 22, 10, 22, 22, 46, 10, 22, 22, 46, 22, 46, 46, 94, 10, 22, 22, 46, 22, 46, 46, 94, 22, 46, 46, 94, 46, 94, 94, 190

Offset: 1

Omar E. Pol, May 25 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, A160720, A160721, A160722.

a(n) = 3*A001316(n-1) - 2

Formula and more terms from Max Alekseyev, Sep 08 2011

A160742 a(n) = A151566(n)*2.

Original entry on oeis.org

0, 2, 4, 8, 12, 16, 20, 28, 36, 40, 44, 52, 60, 68, 76, 92, 108, 112, 116, 124, 132, 140, 148, 164, 180, 188, 196, 212, 228, 244, 260, 292, 324, 328, 332, 340, 348, 356, 364, 380, 396, 404, 412, 428, 444, 460, 476, 508, 540, 548, 556, 572, 588, 604, 620, 652, 684

Offset: 0

Omar E. Pol, May 25 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, A151566, A160720, A160722, A160736, A160738, A160740, A160744, A160746.

More terms from Jinyuan Wang, Mar 14 2020

A160746 a(n) = A151566(n)*4.

Original entry on oeis.org

0, 4, 8, 16, 24, 32, 40, 56, 72, 80, 88, 104, 120, 136, 152, 184, 216, 224, 232, 248, 264, 280, 296, 328, 360, 376, 392, 424, 456, 488, 520, 584, 648, 656, 664, 680, 696, 712, 728, 760, 792, 808, 824, 856, 888, 920, 952, 1016, 1080, 1096, 1112, 1144, 1176, 1208, 1240

Offset: 0

Omar E. Pol, May 25 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, A151566, A160720, A160722, A160736, A160738, A160740, A160742, A160744.

More terms from N. J. A. Sloane, May 25 2009

A262620 Number of "ON" cells at n-th stage in simple 2-dimensional cellular automaton on the square grid (see Comments lines for definition).

Original entry on oeis.org

1, 5, 17, 21, 49, 69, 81, 85, 145, 197, 241, 277, 305, 325, 337, 341, 465, 581, 689, 789, 881, 965, 1041, 1109, 1169, 1221, 1265, 1301, 1329, 1349, 1361, 1365, 1617, 1861, 2097, 2325, 2545, 2757, 2961, 3157, 3345, 3525, 3697, 3861, 4017, 4165, 4305, 4437, 4561, 4677, 4785, 4885, 4977, 5061, 5137, 5205, 5265, 5317, 5361, 5397

Offset: 0

Omar E. Pol, Oct 16 2015

On the infinite square grid consider four 90-degree wedges forming a "X" with the vertex located at the center of a cell.
At stage 0 we start with an ON cell in the vertex of the wedges, so a(0) = 1.
In order to construct the structure we use the following rules for the South wedge:
- The cells turned ON remain ON forever.
- At stage 1 we turn ON the nearest cell to the initial ON cell.
- If n is a power of 2, at stage n we turn "ON" 2*n - 1 connected cells in the n-th row of the wedge.
- Otherwise, if n is not a power of 2, at stage n we turn "ON" k - 2 connected cells in the n-th row of the wedge, where k is the number of ON cells in row n - 1.
- The "ON" cells of row n must be centered respect to the "ON" cells of row n - 1.
The structures in the other three wedges are copies of the structure in the South wedge but they grow in direction East, North and West.
Note that in every wedge the structure seems to grow into the holes of a virtual structure similar to the Sierpiński's triangle but using square cells.
A262621 gives the number of cells turned "ON" at n-th stage.
This is analog of A256266, but here we are working on the square grid and we have four wedges, not six wedges.

			Illustration of the structure after 15 generations:
.
.                                   O
.                                 O O O
.                               O O O O O
.                             O O O O O O O
.                           O O O O O O O O O
.                         O O O O O O O O O O O
.                       O O O O O O O O O O O O O
.                     O O O O O O O O O O O O O O O
.                   O               O               O
.                 O O             O O O             O O
.               O O O           O O O O O           O O O
.             O O O O         O O O O O O O         O O O O
.           O O O O O       O       O       O       O O O O O
.         O O O O O O     O O     O O O     O O     O O O O O O
.       O O O O O O O   O O O   O   O   O   O O O   O O O O O O O
.     O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O
.       O O O O O O O   O O O   O   O   O   O O O   O O O O O O O
.         O O O O O O     O O     O O O     O O     O O O O O O
.           O O O O O       O       O       O       O O O O O
.             O O O O         O O O O O O O         O O O O
.               O O O           O O O O O           O O O
.                 O O             O O O             O O
.                   O               O               O
.                     O O O O O O O O O O O O O O O
.                       O O O O O O O O O O O O O
.                         O O O O O O O O O O O
.                           O O O O O O O O O
.                             O O O O O O O
.                               O O O O O
.                                 O O O
.                                   O
.
There are 341 ON cells in the structure, so a(15) = 341.
Note that every circle in the structure should be replaced with a square cell.

Cf. A147562, A160720, A256266, A261692, A261693, A262621.

a(n) = 1 + 4*A261692(n).

A299776 a(n) = 1 + 4*(A160120(n) - 1)/3.

Original entry on oeis.org

0, 1, 5, 9, 21, 25, 37, 49, 77, 89, 101, 113, 141, 161, 189, 225, 293, 329, 341, 353, 381, 401, 429, 465, 533, 577, 605, 641, 709, 777, 853, 945, 1101, 1209, 1237, 1249, 1277, 1297, 1325, 1361, 1429, 1473, 1501, 1537, 1605, 1673, 1749, 1841, 1997, 2113, 2157

Offset: 0

Omar E. Pol, Apr 03 2018

nonn

Essentially this should be the 120-degree wedge of the cellular automaton of A160120 projected in four quadrants.

First differs from both A147552 and A160720 at a(9).

Shawn A. Broyles, Table of n, a(n) for n = 0..1000

Cf. A139250, A147552, A160120. A160720.

cp's OEIS Frontend

A160744 a(n) = A151566(n)*3.

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A160723 First differences of A160722.

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A160742 a(n) = A151566(n)*2.

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A160746 a(n) = A151566(n)*4.

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A262620 Number of "ON" cells at n-th stage in simple 2-dimensional cellular automaton on the square grid (see Comments lines for definition).

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Formula

A299776 a(n) = 1 + 4*(A160120(n) - 1)/3.

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