A180001 -id:A180001 - cp's OEIS frontend

A334504 Eventual period of a single cell in rule 26 cellular automaton in a cyclic universe of width n.

1, 1, 6, 1, 20, 2, 28, 1, 72, 6, 88, 4, 104, 14, 120, 1, 272, 14, 304, 12, 336, 62, 368, 8, 400, 126, 432, 28, 464, 30, 496, 1, 1056, 30, 1120, 28, 1184, 1022, 1248, 24, 1312, 126, 1376, 124, 1440, 4094, 1504, 16, 1568, 2046, 1632, 252, 1696, 1022, 1760

Offset: 1

N. J. A. Sloane, May 05 2020

nonn

Bradley Klee computed a(1)-a(10).

Bradley Klee, Posting to Math Fun Mailing List, Apr 26 2020

Bert Dobbelaere, Table of n, a(n) for n = 1..120

Cf. A180001, A334496, A334499-A334515, A070939, A268754, A363121.

It seems that a(2*n+2) = A268754(n) and a(2*n+1) = (2*n+1) * 2^A070939(n) = A363121(n+1)/2 for n > 0. - Andrey Zabolotskiy, Sep 04 2024

a(11)-a(40) from Jinyuan Wang, May 09 2020

More terms from Bert Dobbelaere, May 09 2020

A334507 Eventual period of a single cell in rule 122 cellular automaton in a cyclic universe of width n.

Original entry on oeis.org

1, 2, 1, 2, 2, 2, 1, 2, 6, 2, 4, 2, 14, 2, 1, 2, 14, 2, 12, 2, 62, 2, 8, 2, 126, 2, 28, 2, 30, 2, 1, 2, 30, 2, 28, 2, 1022, 2, 24, 2, 126, 2, 124, 2, 4094, 2, 16, 2, 2046, 2, 252, 2, 1022, 2, 56, 2, 32766, 2, 60, 2, 62, 2, 1, 2, 62, 2, 60, 2, 8190, 2

Offset: 1

N. J. A. Sloane, May 05 2020

nonn

Bradley Klee computed a(1)-a(10).

Bradley Klee, Posting to Math Fun Mailing List, Apr 26 2020

Bert Dobbelaere, Table of n, a(n) for n = 1..120

Cf. A180001, A334496, A334499-A334515.

a(11)-a(40) from Jinyuan Wang, May 09 2020

More terms from Bert Dobbelaere, May 09 2020

A334502 Eventual period of a single cell in rule 62 cellular automaton in a cyclic universe of width n.

Original entry on oeis.org

1, 1, 1, 8, 5, 3, 14, 3, 3, 3, 3, 3, 26, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3

Offset: 1

N. J. A. Sloane, May 05 2020

nonn

Bradley Klee computed a(1)-a(10).

Bradley Klee, Posting to Math Fun Mailing List, Apr 26 2020

Index entries for linear recurrences with constant coefficients, signature (1).

Cf. A180001, A334496, A334499-A334515.

Conjectures from Colin Barker, May 13 2020: (Start)
G.f.: x*(1 + 7*x^3 - 3*x^4 - 2*x^5 + 11*x^6 - 11*x^7 + 23*x^12 - 23*x^13) / (1 - x).
a(n) = a(n-1) for n>14.
(End)

More terms from Bert Dobbelaere, May 09 2020

A334505 Eventual period of a single cell in rule 169 cellular automaton in a cyclic universe of width n.

Original entry on oeis.org

1, 2, 1, 2, 15, 1, 49, 15, 54, 205, 176, 1, 403, 441, 450, 2688, 2533, 216, 13471, 5240, 798, 14344, 9108, 1, 3175, 3315, 3402, 28518, 504252, 1800, 2228621, 473792, 941952, 2533, 4485250, 864, 7065594, 646, 357084, 132961360, 200241868, 3192, 2825692, 355342152

Offset: 1

N. J. A. Sloane, May 05 2020

nonn

Bradley Klee computed a(1)-a(10).

Bradley Klee, Posting to Math Fun Mailing List, Apr 26 2020

Bert Dobbelaere, Table of n, a(n) for n = 1..60

Cf. A180001, A334496, A334499-A334515.

a(11)-a(15) from Jinyuan Wang, May 09 2020
a(16)-a(18) from Vaclav Kotesovec, May 10 2020
More terms from Bert Dobbelaere, May 11 2020

A334512 Eventual period of a single cell in rule 105 cellular automaton in a cyclic universe of width n.

Original entry on oeis.org

2, 2, 2, 2, 6, 2, 14, 4, 14, 6, 62, 2, 42, 14, 30, 8, 30, 14, 1022, 12, 126, 62, 4094, 4, 2046, 42, 1022, 28, 32766, 30, 62, 16, 62, 30, 8190, 28, 58254, 1022, 8190, 24, 2046, 126, 254, 124, 8190, 4094, 16777214, 8, 4194302, 2046, 510, 84, 134217726, 1022, 2097150, 56, 1022, 32766

Offset: 1

N. J. A. Sloane, May 05 2020

nonn

Bradley Klee computed a(1)-a(10).

Bradley Klee, Posting to Math Fun Mailing List, Apr 26 2020

Bert Dobbelaere, Table of n, a(n) for n = 1..82

Cf. A180001, A334496, A334499-A334515.

a(11)-a(20) from Jinyuan Wang, May 09 2020
a(21)-a(28) from Vaclav Kotesovec, May 10 2020
More terms from Bert Dobbelaere, May 11 2020

A334514 Eventual period of a single cell in rule 107 cellular automaton in a cyclic universe of width n.

Original entry on oeis.org

2, 2, 3, 2, 15, 2, 28, 2, 36, 20, 11, 12, 117, 28, 60, 8, 68, 36, 76, 20, 84, 44, 92, 24, 100, 52, 108, 28, 116, 60, 124, 32, 132, 68, 140, 36, 148, 76, 156, 40, 164, 84, 172, 44, 180, 92, 188, 48, 196, 100, 204, 52, 212, 108, 220, 56, 228, 116, 236, 60, 244, 124

Offset: 1

N. J. A. Sloane, May 05 2020

nonn

Bradley Klee computed a(1)-a(10).

Bradley Klee, Posting to Math Fun Mailing List, Apr 26 2020

Cf. A180001, A334496, A334499-A334515.

Conjectures from Colin Barker, May 09 2020: (Start)
G.f.: x*(2 + 2*x + 3*x^2 + 2*x^3 + 11*x^4 - 2*x^5 + 22*x^6 - 2*x^7 + 8*x^8 + 18*x^9 - 42*x^10 + 10*x^11 + 60*x^12 - 10*x^13 + 66*x^14 - 14*x^15 - 130*x^16 - 33*x^18 + 16*x^19 + 65*x^20 - 8*x^23) / ((1 - x)^2*(1 + x)^2*(1 + x^2)^2).
a(n) = 2*a(n-4) - a(n-8) for n>24.
(End)

More terms from Jinyuan Wang, May 09 2020

A319780 a(n) is the period of cyclic structures that appear in the 3-state (0,1,2) 1D cellular automaton started from a single cell at state 1 with rule n.

Original entry on oeis.org

2, 2, 1, 0, 2, 1, 0, 2, 1, 2, 0, 1, 0, 0, 2, 0, 0, 1, 2, 0, 1, 0, 0, 1, 0, 0, 1, 2, 2, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 1, 0, 2, 1, 0, 2, 1

Offset: 1

Philipp O. Tsvetkov, Sep 27 2018

The length of the sequence is equal to 3^3^3 = 7625597484987.

			1D cellular automaton with rule=1 gives the following generations:
   1  ..........1.......... <------ start
   2  111111111...111111111 <------ end
   3  ..........1..........
   4  111111111...111111111
   5  ..........1..........
   6  111111111...111111111
   7  ..........1..........
The period is 2, thus a(1) = 2.
For rule=150:
   1  ..........1..... <------ start
   2  .........22..... <------ end
   3  ........1.......
   4  .......22.......
   5  ......1.........
   6  .....22.........
   7  ....1...........
The period is 2, thus a(150) = 2.
For rule=100000000797:
   1  .........1....... <------ start
   2  ........2.2......
   3  ........111......
   4  .......2.112.....
   5  .......12........
   6  ......21.........
   7  ........2........ <------ end
   8  ........1........
   9  .......2.2.......
  10  .......111.......
  11  ......2.112......
  12  ......12.........
  13  .....21..........
  14  .......2.........
  15  .......1.........
The period is 7, thus a(100000000797) = 7.
a(10032729) = 12.
a(10096524) = 16.

Cf. A180001.

Table[
  Length[
  Last[
   FindTransientRepeat[(Internal`DeleteTrailingZeros[
        Reverse[Internal`DeleteTrailingZeros[#]]]) & /@
     CellularAutomaton[{i, 3}, {ConstantArray[0, 25], {1}, ConstantArray[0, 25]} // Flatten, 50], 2]]],
{i, 1, 1000}
]

A334501 Eventual period of a single cell in rule 190 cellular automaton in a cyclic universe of width n.

Original entry on oeis.org

1, 1, 1, 4, 5, 6, 7, 4, 9, 10, 11, 4, 13, 14, 15, 4, 17, 18, 19, 4, 21, 22, 23, 4, 25, 26, 27, 4, 29, 30, 31, 4, 33, 34, 35, 4, 37, 38, 39, 4, 41, 42, 43, 4, 45, 46, 47, 4, 49, 50, 51, 4, 53, 54, 55, 4, 57, 58, 59, 4, 61, 62, 63, 4, 65, 66, 67, 4, 69, 70

Offset: 1

N. J. A. Sloane, May 05 2020

nonn

Bradley Klee computed a(1)-a(10).

Bradley Klee, Posting to Math Fun Mailing List, Apr 26 2020

Cf. A085587, A180001, A334496, A334502-A334515.

Conjectures from Colin Barker, May 09 2020: (Start)
G.f.: x*(1 + x + x^2 + 4*x^3 + 3*x^4 + 4*x^5 + 5*x^6 - 4*x^7 - x^9 - 2*x^10) / ((1 - x)^2*(1 + x)^2*(1 + x^2)^2).
a(n) = 2*a(n-4) - a(n-8) for n>8.
(End)

More terms from Bert Dobbelaere, May 09 2020

A334503 Eventual period of a single cell in rule 131 cellular automaton in a cyclic universe of width n.

Original entry on oeis.org

1, 1, 3, 8, 3, 3, 14, 16, 3, 20, 3, 3, 3, 3, 3, 32, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3

Offset: 1

N. J. A. Sloane, May 05 2020

nonn

Bradley Klee computed a(1)-a(10).

Bradley Klee, Posting to Math Fun Mailing List, Apr 26 2020

Index entries for linear recurrences with constant coefficients, signature (1).

Cf. A180001, A334496, A334499-A334515.

Conjectures from Colin Barker, May 13 2020: (Start)
G.f.: x*(1 + 2*x^2 + 5*x^3 - 5*x^4 + 11*x^6 + 2*x^7 - 13*x^8 + 17*x^9 - 17*x^10 + 29*x^15 - 29*x^16) / (1 - x).
a(n) = a(n-1) for n>17.
(End)

More terms from Jinyuan Wang, May 09 2020

A334509 Eventual period of a single cell in rule 41 cellular automaton in a cyclic universe of width n.

Original entry on oeis.org

2, 2, 2, 2, 15, 2, 28, 8, 36, 20, 44, 12, 52, 28, 60, 16, 68, 36, 76, 20, 84, 44, 92, 24, 100, 52, 108, 28, 116, 60, 124, 32, 132, 68, 140, 36, 148, 76, 156, 40, 164, 84, 172, 44, 180, 92, 188, 48, 196, 100, 204, 52, 212, 108, 220, 56, 228, 116, 236, 60, 244, 124

Offset: 1

N. J. A. Sloane, May 05 2020

nonn

Bradley Klee computed a(1)-a(10).

Bradley Klee, Posting to Math Fun Mailing List, Apr 26 2020.

Wolfram Research, Rule 41 - Wolfram Atlas of Simple Programs

Cf. A176895, A180001, A334496, A334499-A334515.

Table[-Subtract @@ Flatten[Map[Position[#, #[[-1]]] &, NestWhileList[CellularAutomaton[41], Prepend[Table[0, {n - 1}], 1], Unequal, All], {0}]],{n,62}] (* Stefano Spezia, Oct 04 2021, after Ben Branman in A180001 *)

Conjectures from Colin Barker, May 09 2020: (Start)
G.f.: x*(2 + 2*x + 2*x^2 + 2*x^3 + 11*x^4 - 2*x^5 + 24*x^6 + 4*x^7 + 8*x^8 + 18*x^9 - 10*x^10 - 2*x^11 - 5*x^12 - 10*x^13) / ((1 - x)^2*(1 + x)^2*(1 + x^2)^2).
a(n) = 2*a(n-4) - a(n-8) for n > 14. (End)
Conjecture: a(n) = n*A176895(n) for n > 6. - Stefano Spezia, Oct 03 2021

More terms from Jinyuan Wang, May 09 2020

cp's OEIS Frontend

A334504 Eventual period of a single cell in rule 26 cellular automaton in a cyclic universe of width n.

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A334507 Eventual period of a single cell in rule 122 cellular automaton in a cyclic universe of width n.

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A334502 Eventual period of a single cell in rule 62 cellular automaton in a cyclic universe of width n.

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A334505 Eventual period of a single cell in rule 169 cellular automaton in a cyclic universe of width n.

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A334512 Eventual period of a single cell in rule 105 cellular automaton in a cyclic universe of width n.

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A334514 Eventual period of a single cell in rule 107 cellular automaton in a cyclic universe of width n.

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A319780 a(n) is the period of cyclic structures that appear in the 3-state (0,1,2) 1D cellular automaton started from a single cell at state 1 with rule n.

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A334501 Eventual period of a single cell in rule 190 cellular automaton in a cyclic universe of width n.

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A334503 Eventual period of a single cell in rule 131 cellular automaton in a cyclic universe of width n.

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