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 1-3 of 3 results.

A071037 Triangle read by rows giving successive states of cellular automaton generated by "Rule 158".

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1
Offset: 0

Views

Author

Hans Havermann, May 26 2002

Keywords

Comments

Row n has length 2n+1.

Examples

			            1;
         1, 1, 1;
      1, 1, 1, 0, 1;
   1, 1, 1, 0, 0, 1, 1;
1, 1, 1, 0, 1, 1, 1, 0, 1;
...

Links

Crossrefs

Cf. A118171 (rows decimal), A265379 (rows binary), A265381 (central column decimal), A265380 (central column binary).

Programs

  • Mathematica
    A071037list[rowmax_]:=MapIndexed[ArrayPad[#1, #2-rowmax-1]&,CellularAutomaton[158,{{1},0},rowmax]];A071037list[10] (* Generates 11 rows *) (* Paolo Xausa, Jul 27 2023 *)

Extensions

Corrected by Hans Havermann, Jan 07 2012

A265380 Binary representation of the middle column of the "Rule 158" elementary cellular automaton starting with a single ON (black) cell.

Original entry on oeis.org

1, 11, 111, 1110, 11101, 111011, 1110111, 11101110, 111011101, 1110111011, 11101110111, 111011101110, 1110111011101, 11101110111011, 111011101110111, 1110111011101110, 11101110111011101, 111011101110111011, 1110111011101110111, 11101110111011101110
Offset: 0

Views

Author

Robert Price, Dec 07 2015

Keywords

Examples

			From _Michael De Vlieger_, Dec 09 2015: (Start)
First 8 rows at left, ignoring "0" outside of range of 1's, the center column values in parentheses, and at right the value of center column cells up to that row :
                        (1)                          -> 1
                      1 (1) 1                        -> 11
                    1 1 (1) 0 1                      -> 111
                  1 1 1 (0) 0 1 1                    -> 1110
                1 1 1 0 (1) 1 1 0 1                  -> 11101
              1 1 1 0 0 (1) 1 0 0 1 1                -> 111011
            1 1 1 0 1 1 (1) 0 1 1 1 0 1              -> 1110111
          1 1 1 0 0 1 1 (0) 0 1 1 0 0 1 1            -> 11101110
        1 1 1 0 1 1 1 0 (1) 1 1 0 1 1 1 0 1          -> 111011101
      1 1 1 0 0 1 1 0 0 (1) 1 0 0 1 1 0 0 1 1        -> 1110111011
    1 1 1 0 1 1 1 0 1 1 (1) 0 1 1 1 0 1 1 1 0 1      -> 11101110111
  1 1 1 0 0 1 1 0 0 1 1 (0) 0 1 1 0 0 1 1 0 0 1 1    -> 111011101110
1 1 1 0 1 1 1 0 1 1 1 0 (1) 1 1 0 1 1 1 0 1 1 1 0 1  -> 1110111011101
(End)

References

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

Links

Crossrefs

Cf. A071037, A265381.

Programs

  • Mathematica
    f[n_] := Block[{w = {}}, Do[AppendTo[w, Boole[Mod[k, 4] != 3]], {k, 0, n}]; FromDigits@ w]; Table[f@ n, {n, 0, 19}] (* Michael De Vlieger, Dec 09 2015 *)

Formula

Conjectures from Colin Barker, Dec 14 2015 and Apr 18 2019: (Start)
a(n) = 10*a(n-1) + a(n-4) - 10*a(n-5) for n>4.
G.f.: (1+x+x^2) / ((1-x)*(1+x)*(1-10*x)*(1+x^2)).
(End)

Extensions

Removed an unjustified claim that Colin Barker's conjectures are correct. Removed 2 programs based on conjectures. - N. J. A. Sloane, Jun 13 2022

A263119 Number of (n+3) X (1+3) 0..1 arrays with each row divisible by 15 and column not divisible by 15, read as a binary number with top and left being the most significant bits.

Original entry on oeis.org

14, 29, 59, 119, 238, 477, 955, 1911, 3822, 7645, 15291, 30583, 61166, 122333, 244667, 489335, 978670, 1957341, 3914683, 7829367, 15658734, 31317469, 62634939, 125269879, 250539758, 501079517, 1002159035, 2004318071, 4008636142
Offset: 1

Views

Author

R. H. Hardin, Oct 10 2015

Keywords

Examples

			Some solutions for n=4:
..0..0..0..0....1..1..1..1....0..0..0..0....0..0..0..0....0..0..0..0
..0..0..0..0....1..1..1..1....1..1..1..1....0..0..0..0....0..0..0..0
..0..0..0..0....1..1..1..1....1..1..1..1....1..1..1..1....1..1..1..1
..0..0..0..0....0..0..0..0....1..1..1..1....0..0..0..0....0..0..0..0
..1..1..1..1....0..0..0..0....0..0..0..0....0..0..0..0....1..1..1..1
..0..0..0..0....1..1..1..1....1..1..1..1....0..0..0..0....1..1..1..1
..0..0..0..0....1..1..1..1....0..0..0..0....1..1..1..1....0..0..0..0

Links

Crossrefs

Column 1 of A263124.

Formula

Empirical: a(n) = 2*a(n-1) + a(n-4) - 2*a(n-5) = A265381(n+2).
Empirical g.f.: x*(14 + x + x^2 + x^3 - 14*x^4) / ((1 - x)*(1 + x)*(1 - 2*x)*(1 + x^2)). - Colin Barker, Jan 01 2019
Showing 1-3 of 3 results.

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

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