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 1-4 of 4 results.

A070952 Number of 1's in n-th generation of 1-D CA using Rule 30, started with a single 1.

Original entry on oeis.org

1, 3, 3, 6, 4, 9, 5, 12, 7, 12, 11, 14, 12, 19, 13, 22, 15, 19, 20, 24, 21, 23, 23, 28, 26, 27, 26, 33, 30, 34, 31, 39, 26, 39, 29, 46, 32, 44, 38, 45, 47, 41, 45, 49, 38, 55, 42, 51, 44, 53, 43, 59, 52, 60, 49, 65, 57, 60, 56, 69, 61, 70, 59, 78, 64, 56, 65, 69, 69
Offset: 0

Views

Author

N. J. A. Sloane, May 19 2002, Aug 10 2009

Keywords

Comments

Number of 1's in n-th row of triangle in A070950.
Row sums in A070950; a(n) = 2*n + 1 - A070951(n). - Reinhard Zumkeller, Jun 07 2013

Examples

			May be arranged into blocks of length 1,1,2,4,8,16,...:
1,
3,
3, 6,
4, 9, 5, 12,
7, 12, 11, 14, 12, 19, 13, 22,
15, 19, 20, 24, 21, 23, 23, 28, 26, 27, 26, 33, 30, 34, 31, 39,
26, 39, 29, 46, 32, 44, 38, 45, 47, 41, 45, 49, 38, 55, 42, 51,
    44, 53, 43, 59, 52, 60, 49, 65, 57, 60, 56, 69, 61, 70, 59, 78,
64, 56, 65, 69, 69, ...

Links

Crossrefs

This sequence, A110240, and A245549 all describe the same sequence of successive states. See also A269160.
Cf. A071049, A070950, A070951, A151929, A051023.
Cf. A110267 (partial sums), A246023, A246024, A246025, A246026, A246597.
A265703 is an essentially identical sequence.

Programs

  • Haskell
    a070952 = sum . a070950_row  -- Reinhard Zumkeller, Jun 07 2013
  • Mathematica
    Map[Function[Apply[Plus,Flatten[ #1]]], CellularAutomaton[30,{{1},0},100]] (* N. J. A. Sloane, Aug 10 2009 *)
SequenceCount[s, {1,0}] + 2 SequenceCount[s, {0,0,1}] (* gives a(n) where s is the sequence for row n-1 *) (* Trevor Cappallo, May 01 2021 *)

Extensions

More terms from Hans Havermann, May 26 2002
Corrected offset and initial term - N. J. A. Sloane, Jun 07 2013

A265704 Total number of OFF (white) cells after n iterations of the "Rule 135" elementary cellular automaton starting with a single ON (black) cell.

Original entry on oeis.org

0, 1, 4, 7, 13, 17, 26, 31, 43, 50, 62, 73, 87, 99, 118, 131, 153, 168, 187, 207, 231, 252, 275, 298, 326, 352, 379, 405, 438, 468, 502, 533, 572, 598, 637, 666, 712, 744, 788, 826, 871, 918, 959, 1004, 1053, 1091, 1146, 1188, 1239, 1283, 1336, 1379, 1438
Offset: 0

Views

Author

Robert Price, Dec 13 2015

Keywords

Comments

This is (apart from an index shift) the same as A110267. The reason is that Rule 135 is obtained from Rule 30 by inverting both colors of the 4 cells correlated by the rules. - R. J. Mathar, Dec 16 2015

References

  • S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.

Links

Crossrefs

Cf. A110267 (essentially the same sequence), A265695.

A261299 Binary representation of the middle column of the "Rule 30" elementary cellular automaton starting with a single ON (black) cell.

Original entry on oeis.org

1, 11, 110, 1101, 11011, 110111, 1101110, 11011100, 110111001, 1101110011, 11011100110, 110111001100, 1101110011000, 11011100110001, 110111001100010, 1101110011000101, 11011100110001011, 110111001100010110, 1101110011000101100, 11011100110001011001
Offset: 0

Views

Author

Robert Price, Dec 05 2015

Keywords

References

  • S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.

Links

Crossrefs

Cf. A070950, A245549, A110240, A051023, A092539, A070952, A110267.

Programs

  • Mathematica
    A261299list[nmax_]:=With[{ca=CellularAutomaton[30,{{1},0},{nmax,{{0}}}]},Array[FromDigits[Take[ca,#]]&,nmax+1]];A261299list[25] (* Paolo Xausa, May 30 2023 *)

A265224 Total number of OFF (white) cells after n iterations of the "Rule 30" elementary cellular automaton starting with a single ON (black) cell.

Original entry on oeis.org

0, 0, 2, 3, 8, 10, 18, 21, 31, 38, 48, 57, 70, 78, 94, 103, 121, 137, 154, 169, 189, 209, 231, 250, 273, 297, 324, 346, 373, 398, 428, 452, 491, 519, 559, 584, 625, 656, 695, 729, 763, 805, 845, 883, 934, 970, 1021, 1065, 1118, 1164, 1222, 1266, 1319, 1366
Offset: 0

Views

Author

Robert Price, Dec 05 2015

Keywords

Comments

Rule 86, the mirror image of Rule 30, also generates this sequence. - Karl V. Keller, Jr., Sep 20 2020

References

  • S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.

Links

Crossrefs

Cf. A051023, A070950, A070951, A070952, A092539, A110240, A110267, A245549.
Showing 1-4 of 4 results.

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

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