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.

Previous Showing 11-16 of 16 results.

A246331 Total number of ON cells at stage 2n of two-dimensional 5-neighbor outer totalistic cellular automaton defined by "Rule 465".

Original entry on oeis.org

1, 9, 25, 49, 89, 113, 161, 233, 345, 369, 417, 489, 609, 681, 825, 1041, 1369, 1393, 1441, 1513, 1633, 1705, 1849, 2065, 2401, 2473, 2617, 2833, 3193, 3409, 3841, 4489, 5465, 5489, 5537, 5609, 5729, 5801, 5945, 6161, 6497, 6569, 6713, 6929, 7289, 7505, 7937
Offset: 0

Views

Author

N. J. A. Sloane, Aug 30 2014

Keywords

Comments

The number of ON cells at stage 2n+1 is infinite.
This is a bisection of A147562.
The sequence b(n) defined by b(n) = number of ON cells at stage n if n is even, b(n) = number of OFF cells at stage n if n is odd coincides with A147562, and has a simple formula.

References

  • S. Wolfram, A New Kind of Science, Wolfram Media, 2002; pp. 173-175.

Links

Crossrefs

Cf. A147562, A169699, A246316, A246318, A246325, A246326, ...

Programs

  • Mathematica
    Map[Function[Apply[Plus, Flatten[ #1]]], CellularAutomaton[{ 465, {2, {{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}}, {1, 1}}, {{{1}}, 0}, 130]] (* then take every other term *)
ArrayPlot /@ CellularAutomaton[{465, {2, {{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}}, {1, 1}}, {{{1}}, 0}, 23]

A253079 a(n) = if n is even, number of ON cells at stage n of two-dimensional 5-neighbor outer totalistic cellular automaton defined by "Rule 489" or if n is odd, number of OFF cells.

Original entry on oeis.org

1, 5, 13, 17, 33, 21, 65, 65, 97, 61, 145, 153, 177, 149, 257, 249, 345, 237, 433, 409, 465, 389, 601, 521, 745, 501, 897, 713, 897, 709, 1081, 921, 1281, 877, 1481, 1121, 1505, 1125, 1817, 1393, 1993, 1309, 2209, 1577, 2401, 1653, 2497, 1953, 2985, 1901
Offset: 0

Views

Author

N. J. A. Sloane, Feb 04 2015

Keywords

Comments

If we subtract 1 and divide by 4, the result (A253080) almost looks like it should have a simple recurrence. It would be nice to know more.

References

  • S. Wolfram, A New Kind of Science, Wolfram Media, 2002; pp. 173-175.

Links

Crossrefs

Cf. A253080, A169699, A246316, A246318, A246325, A246326, ...

Programs

  • Mathematica
    Map[Function[Apply[Plus, Flatten[ #1]]], CellularAutomaton[{ 489, {2, {{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}}, {1, 1}}, {{{1}}, 0}, 200]] (* then subtract the odd-indexed terms from 201^2 (a constant which depends on Mathematica's choice of grid size) *)
ArrayPlot /@ CellularAutomaton[{489, {2, {{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}}, {1, 1}}, {{{1}}, 0}, 23]

A246327 Total number of ON cells at stage 2n of two-dimensional 5-neighbor outer totalistic cellular automaton defined by "Rule 457".

Original entry on oeis.org

1, 9, 21, 57, 65, 81, 97, 165, 233, 221, 277, 361, 425, 441, 585, 777, 905, 777, 933, 1045, 1173, 1225, 1593, 1833, 1981, 1725, 1757, 2429, 2365, 2701, 2881, 3093, 3361, 3345, 3353, 3397, 3861, 4057, 4421, 4549, 4765, 5053, 5373, 5713, 5685, 5769, 6161, 6933, 7325, 7029, 7533, 7757, 8329, 7853
Offset: 0

Views

Author

N. J. A. Sloane, Aug 30 2014

Keywords

Comments

The number of ON cells at stage 2n+1 is infinite.

References

  • S. Wolfram, A New Kind of Science, Wolfram Media, 2002; pp. 173-175.

Links

Crossrefs

Cf. A169699, A246316, A246318, A246325, A246326.

Programs

  • Mathematica
    Map[Function[Apply[Plus, Flatten[ #1]]], CellularAutomaton[{ 457, {2, {{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}}, {1, 1}}, {{{1}}, 0}, 130]] (* then take every other term *)
ArrayPlot /@ CellularAutomaton[{457, {2, {{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}}, {1, 1}}, {{{1}}, 0}, 23]

A246328 Total number of ON cells at stage 2n of two-dimensional 5-neighbor outer totalistic cellular automaton defined by "Rule 459".

Original entry on oeis.org

1, 9, 25, 32, 101, 57, 156, 153, 309, 185, 389, 345, 613, 460, 669, 721, 1120, 961, 965, 1104, 1337, 1237, 1500, 1524, 2136, 1824, 2232, 2260, 2640, 2649, 2736, 3092, 3689, 3144, 3688, 3932, 3937, 4228, 4488, 5013, 5112, 5012, 5748, 5945, 6440, 6216, 7073, 7396, 7932, 7412, 8201, 8348, 8696, 9237
Offset: 0

Views

Author

N. J. A. Sloane, Aug 30 2014

Keywords

Comments

The number of ON cells at stage 2n+1 is infinite.

References

  • S. Wolfram, A New Kind of Science, Wolfram Media, 2002; pp. 173-175.

Links

Crossrefs

Cf. A169699, A246316, A246318, A246325, A246326, ...

Programs

  • Mathematica
    Map[Function[Apply[Plus, Flatten[ #1]]], CellularAutomaton[{ 459, {2, {{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}}, {1, 1}}, {{{1}}, 0}, 130]] (* then take every other term *)
ArrayPlot /@ CellularAutomaton[{459, {2, {{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}}, {1, 1}}, {{{1}}, 0}, 23]

A246332 a(n) = if n is even, number of ON cells at stage n of two-dimensional 5-neighbor outer totalistic cellular automaton defined by "Rule 461" or if n is odd, number of OFF cells.

Original entry on oeis.org

1, 1, 5, 5, 17, 9, 21, 21, 25, 33, 45, 49, 81, 69, 105, 81, 101, 101, 165, 141, 197, 185, 217, 209, 265, 245, 337, 269, 405, 325, 477, 389, 521, 461, 625, 469, 621, 485, 769, 585, 849, 737, 825, 705, 973, 713, 985, 841, 1089, 925, 1257, 969, 1229, 1093, 1265
Offset: 0

Views

Author

N. J. A. Sloane, Aug 30 2014

Keywords

References

  • S. Wolfram, A New Kind of Science, Wolfram Media, 2002; pp. 173-175.

Links

Crossrefs

A246329 is a bisection.
Cf. A169699, A246316, A246318, A246325, A246326, ...

Programs

  • Mathematica
    Map[Function[Apply[Plus, Flatten[ #1]]], CellularAutomaton[{ 461, {2, {{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}}, {1, 1}}, {{{1}}, 0}, 130]] (* then subtract the odd-indexed terms from 131^2 *)
ArrayPlot /@ CellularAutomaton[{461, {2, {{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}}, {1, 1}}, {{{1}}, 0}, 23]

A272700 Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 510", based on the 5-celled von Neumann neighborhood.

Original entry on oeis.org

1, 6, 18, 43, 71, 127, 183, 296, 356, 476, 596, 836, 956, 1196, 1436, 1917, 2041, 2289, 2537, 3033, 3281, 3777, 4273, 5265, 5513, 6009, 6505, 7497, 7993, 8985, 9977, 11962, 12214, 12718, 13222, 14230, 14734, 15742, 16750, 18766, 19270, 20278, 21286, 23302
Offset: 0

Views

Author

Robert Price, May 04 2016

Keywords

Comments

Initialized with a single black (ON) cell at stage zero.

References

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

Links

Crossrefs

Cf. A169699.

Programs

  • Mathematica
    CAStep[rule_,a_]:=Map[rule[[10-#]]&,ListConvolve[{{0,2,0},{2,1,2},{0,2,0}},a,2],{2}];
code=510; 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}];
on=Map[Function[Apply[Plus,Flatten[#1]]],ca] (* Count ON cells at each stage *)
Table[Total[Part[on,Range[1,i]]],{i,1,Length[on]}] (* Sum at each stage *)
Previous Showing 11-16 of 16 results.

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

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