cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-2 of 2 results.

A204371 Maximum period of cellular automaton rule 110 in a cyclic universe of width n.

Original entry on oeis.org

1, 1, 1, 2, 1, 9, 14, 16, 7, 25, 110, 18, 351, 91, 295, 32, 578, 81, 285, 240, 630, 462, 1058, 552, 300, 351, 567, 2156, 1044, 1770, 2759, 2368, 1100, 969, 3920, 1584
Offset: 1

Views

Author

Ben Branman, Jan 14 2012

Keywords

Comments

a(n) >= A180001(n), and this sequence agrees with A180001 up to n=11.

Examples

			The 12 cell pattern
000100110111
001101111101
011111000111
110001001101
010011011111
110111110001
011100010011
110100110111
011101111100
110111000100
111101001101
000111011111
001101110001
011111010011
110001110111
010011011100
110111110100
111100011101
000100110111
Has period 18, which is the maximum possible, so a(12)=18

Links

Crossrefs

Cf. A180001, A161903, A006978, A332717, A332718.

Programs

  • Mathematica
    f[list_] := -Subtract @@ Flatten[Map[Position[#, #[[-1]]] &, NestWhileList[CellularAutomaton[110], list, Unequal, All], {0}]]; ma[n_] := Max[Table[f[IntegerDigits[i, 2, n]], {i, 0, 2^n - 1}]]; Table[ma[n], {n, 1, 10}]

Extensions

a(19)-a(36) from Lars Blomberg, Dec 24 2015

A332717 Triangle read by rows in which row n lists the possible eventual periods of cellular automaton rule 110 in a cyclic universe of width n.

Original entry on oeis.org

1, 1, 1, 1, 2, 1, 1, 9, 1, 14, 1, 2, 8, 16, 1, 3, 7, 1, 5, 15, 25, 1, 7, 110, 1, 2, 9, 18, 1, 351, 1, 7, 12, 14, 21, 91, 1, 295, 1, 2, 8, 16, 24, 32, 1, 7, 119, 578, 1, 3, 7, 9, 27, 81, 1, 190, 285, 1, 2, 5, 7, 15, 25, 30, 50, 200, 240, 1, 14, 21, 189, 315, 630
Offset: 1

Views

Author

Hans Havermann, Jun 08 2020

Keywords

Comments

Frequency of occurrence for the first 73 terms (semicolons separate rows): 2; 4; 8; 4, 12; 32; 10, 54; 9, 119; 20, 12, 8, 216; 17, 18, 477; 134, 220, 130, 540; 35, 495, 1518; 34, 12, 3426, 624; 54, 8138; 67, 8442, 644, 371, 168, 6692; 113, 32655; 116, 12, 8, 680, 1920, 62800; 138, 93330, 15895, 21709; 181, 36, 2349, 57024, 198594, 3960; 249, 28481, 495558; 534, 12, 3040, 49700, 270, 3300, 614140, 30660, 342380, 4540; 414, 455, 42, 7938, 331590, 1756713. Note that the sum of the frequencies of row n is 2^n.

Examples

			Triangle begins:
  1
  1
  1
  1    2
  1
  1    9
  1   14
  1    2    8   16
  1    3    7
  1    5   15   25
  1    7  110
  1    2    9   18
  1  351
  1    7   12   14   21   91
  1  295
  1    2    8   16   24   32
  1    7  119  578
  1    3    7    9   27   81
  1  190  285
  1    2    5    7   15   25   30   50  200  240
  1   14   21  189  315  630

Crossrefs

Cf. A332718 (row lengths), A204371 (final terms for each row).
Showing 1-2 of 2 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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