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.

A287196 Binary representation of the diagonal from the origin to the corner of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 259", based on the 5-celled von Neumann neighborhood.

Original entry on oeis.org

1, 11, 100, 11, 10000, 1111, 1000000, 111111, 100000000, 11111111, 10000000000, 1111111111, 1000000000000, 111111111111, 100000000000000, 11111111111111, 10000000000000000, 1111111111111111, 1000000000000000000, 111111111111111111, 100000000000000000000
Offset: 0

Views

Author

Robert Price, May 21 2017

Keywords

Comments

Initialized with a single black (ON) cell at stage zero.
Seems to differ from A277798 only at n=1. - R. J. Mathar, May 28 2025

References

  • S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.

Links

Crossrefs

Cf. A287194, A287197, A287199.

Programs

  • Mathematica
    CAStep[rule_, a_] := Map[rule[[10 - #]] &, ListConvolve[{{0, 2, 0},{2, 1, 2}, {0, 2, 0}}, a, 2],{2}];
code = 259; stages = 128;
rule = IntegerDigits[code, 2, 10];
g = 2 * stages + 1; (* Maximum size of grid *)
a = PadLeft[{{1}}, {g, g}, 0,Floor[{g, g}/2]]; (* Initial ON cell on grid *)
ca = a;
ca = Table[ca = CAStep[rule, ca], {n, 1, stages + 1}];
PrependTo[ca, a];
(* Trim full grid to reflect growth by one cell at each stage *)
k = (Length[ca[[1]]] + 1)/2;
ca = Table[Table[Part[ca[[n]] [[j]],Range[k + 1 - n, k - 1 + n]], {j, k + 1 - n, k - 1 + n}], {n, 1, k}];
Table[FromDigits[Part[ca[[i]] [[i]], Range[i, 2 * i - 1]], 10], {i, 1, stages - 1}]

A287197 Decimal representation of the diagonal from the corner to the origin of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 259", based on the 5-celled von Neumann neighborhood.

Original entry on oeis.org

1, 3, 1, 12, 1, 60, 1, 252, 1, 1020, 1, 4092, 1, 16380, 1, 65532, 1, 262140, 1, 1048572, 1, 4194300, 1, 16777212, 1, 67108860, 1, 268435452, 1, 1073741820, 1, 4294967292, 1, 17179869180, 1, 68719476732, 1, 274877906940, 1, 1099511627772, 1, 4398046511100, 1
Offset: 0

Views

Author

Robert Price, May 21 2017

Keywords

Comments

Initialized with a single black (ON) cell at stage zero.
Appears to differ from A277799 only at a(1). - R. J. Mathar, May 25 2017

References

  • S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.

Links

Crossrefs

Cf. A287194, A287196, A287199.

Programs

  • Mathematica
    CAStep[rule_, a_] := Map[rule[[10 - #]] &, ListConvolve[{{0, 2, 0},{2, 1, 2}, {0, 2, 0}}, a, 2],{2}];
code = 259; stages = 128;
rule = IntegerDigits[code, 2, 10];
g = 2 * stages + 1; (* Maximum size of grid *)
a = PadLeft[{{1}}, {g, g}, 0,Floor[{g, g}/2]]; (* Initial ON cell on grid *)
ca = a;
ca = Table[ca = CAStep[rule, ca], {n, 1, stages + 1}];
PrependTo[ca, a];
(* Trim full grid to reflect growth by one cell at each stage *)
k = (Length[ca[[1]]] + 1)/2;
ca = Table[Table[Part[ca[[n]] [[j]],Range[k + 1 - n, k - 1 + n]], {j, k + 1 - n, k - 1 + n}], {n, 1, k}];
Table[FromDigits[Part[ca[[i]] [[i]], Range[i, 2 * i - 1]], 10], {i, 1, stages - 1}]

A287199 Decimal representation of the diagonal from the origin to the corner of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 259", based on the 5-celled von Neumann neighborhood.

Original entry on oeis.org

1, 3, 4, 3, 16, 15, 64, 63, 256, 255, 1024, 1023, 4096, 4095, 16384, 16383, 65536, 65535, 262144, 262143, 1048576, 1048575, 4194304, 4194303, 16777216, 16777215, 67108864, 67108863, 268435456, 268435455, 1073741824, 1073741823, 4294967296, 4294967295
Offset: 0

Views

Author

Robert Price, May 21 2017

Keywords

Comments

Initialized with a single black (ON) cell at stage zero.
Appears to differ from A277800 only at a(1). - R. J. Mathar, May 25 2017

References

  • S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.

Links

Crossrefs

Cf. A287194, A287196, A287197.

Programs

  • Mathematica
    CAStep[rule_, a_] := Map[rule[[10 - #]] &, ListConvolve[{{0, 2, 0},{2, 1, 2}, {0, 2, 0}}, a, 2],{2}];
code = 259; stages = 128;
rule = IntegerDigits[code, 2, 10];
g = 2 * stages + 1; (* Maximum size of grid *)
a = PadLeft[{{1}}, {g, g}, 0,Floor[{g, g}/2]]; (* Initial ON cell on grid *)
ca = a;
ca = Table[ca = CAStep[rule, ca], {n, 1, stages + 1}];
PrependTo[ca, a];
(* Trim full grid to reflect growth by one cell at each stage *)
k = (Length[ca[[1]]] + 1)/2;
ca = Table[Table[Part[ca[[n]] [[j]],Range[k + 1 - n, k - 1 + n]], {j, k + 1 - n, k - 1 + n}], {n, 1, k}];
Table[FromDigits[Part[ca[[i]] [[i]], Range[i, 2 * i - 1]], 10], {i, 1, stages - 1}]

Formula

Conjectures from Colin Barker, May 25 2017: (Start)
G.f.: (1 + 3*x - x^2 - 12*x^3 + 12*x^5) / ((1 - x)*(1 + x)*(1 - 2*x)*(1 + 2*x)).
a(n) = 2^n for n>1 and even.
a(n) = 2^(n-1) - 1 for n odd.
a(n) = 5*a(n-2) - 4*a(n-4) for n>3.
(End)
Showing 1-3 of 3 results.

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

Content is available under The OEIS End-User License Agreement.