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 1-10 of 12 results. Next

A246333 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 493" or if n is odd, number of OFF cells.

Original entry on oeis.org

1, 1, 5, 5, 17, 9, 29, 21, 61, 25, 73, 37, 109, 57, 157, 85, 229, 89, 241, 101, 277, 121, 329, 165, 429, 169, 477, 213, 573, 217, 633, 317, 861, 321, 873, 333, 909, 353, 961, 397, 1061, 401, 1113, 461, 1237, 481, 1353, 637, 1645, 593, 1661, 733, 1893, 689, 1969, 877, 2325, 801, 2321, 981, 2669, 921, 2693, 1157, 3245, 1185, 3305, 1197, 3341, 1217, 3393, 1261, 3493
Offset: 0

Views

Author

N. J. A. Sloane, Aug 30 2014

Keywords

Comments

More than the usual number of terms are shown in order to distinguish this from a closely related entry.

References

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

Links

Crossrefs

Bisections: A246334, A246335.
Cf. A169699, A246316, A246318, A246325, A246326, ...

Programs

  • Mathematica
    Map[Function[Apply[Plus, Flatten[ #1]]], CellularAutomaton[{ 493, {2, {{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}}, {1, 1}}, {{{1}}, 0}, 200]] (* then subtract the odd-indexed terms from 201^2 *)
ArrayPlot /@ CellularAutomaton[{493, {2, {{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}}, {1, 1}}, {{{1}}, 0}, 23]

A246330 Total number of ON cells at stage n of two-dimensional 5-neighbor outer totalistic cellular automaton defined by "Rule 462".

Original entry on oeis.org

1, 5, 8, 21, 20, 32, 48, 65, 56, 84, 84, 112, 136, 196, 216, 297, 244, 300, 308, 268, 356, 396, 468, 572, 524, 544, 616, 744, 796, 900, 960, 1145, 1012, 1084, 1052, 1120, 1188, 1268, 1476, 1592, 1668, 1620, 1784, 1776, 1860, 2040, 2144, 2504, 2484, 2416, 2472, 2608, 2572, 2832, 3008, 3292, 3172, 3384, 3460, 3524, 3792
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

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

Programs

  • Mathematica
    Map[Function[Apply[Plus, Flatten[ #1]]], CellularAutomaton[{ 462, {2, {{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}}, {1, 1}}, {{{1}}, 0}, 130]]
ArrayPlot /@ CellularAutomaton[{462, {2, {{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}}, {1, 1}}, {{{1}}, 0}, 23]

A253078 Total number of ON cells at stage n of two-dimensional 5-neighbor outer totalistic cellular automaton defined by "Rule 470".

Original entry on oeis.org

1, 5, 8, 24, 21, 56, 32, 89, 65, 140, 96, 201, 149, 260, 200, 297, 293, 376, 368, 453, 461, 564, 532, 685, 665, 804, 764, 929, 913, 1052, 1060, 1145, 1177, 1296, 1405, 1405, 1404, 1672, 1521, 1845, 1696, 2052, 1909, 2217, 2152, 2416, 2361, 2529, 2644, 2776, 2813, 3053, 2908, 3316, 3093, 3461, 3512, 3792, 3713, 4021
Offset: 0

Views

Author

N. J. A. Sloane, Feb 04 2015

Keywords

Comments

It would be nice to have a formula or recurrence.

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[{ 470, {2, {{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}}, {1, 1}}, {{{1}}, 0}, 130]]
ArrayPlot /@ CellularAutomaton[{470, {2, {{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}}, {1, 1}}, {{{1}}, 0}, 23]

A246329 Total number of ON cells at stage 2n of two-dimensional 5-neighbor outer totalistic cellular automaton defined by "Rule 461".

Original entry on oeis.org

1, 5, 17, 21, 25, 45, 81, 105, 101, 165, 197, 217, 265, 337, 405, 477, 521, 625, 621, 769, 849, 825, 973, 985, 1089, 1257, 1229, 1265, 1401, 1557, 1677, 1713, 2081, 2053, 2177, 2361, 2389, 2669, 2621, 2973, 2901, 3233, 3249, 3529, 3809, 3893, 3765, 3905, 4409, 4657, 4757, 4797, 5321, 5261, 5769, 5757, 5997, 6565, 6597, 6765
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

A bisection of A246332.
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 take every other term *)
ArrayPlot /@ CellularAutomaton[{461, {2, {{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}}, {1, 1}}, {{{1}}, 0}, 23]

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]

A272278 Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 454", based on the 5-celled von Neumann neighborhood.

Original entry on oeis.org

1, 6, 10, 30, 39, 76, 104, 161, 190, 262, 334, 479, 576, 741, 898, 1131, 1272, 1521, 1726, 2015, 2284, 2717, 3145, 3649, 3986, 4474, 4922, 5631, 6192, 6897, 7605, 8585, 9318, 10214, 11106, 12030, 12906, 14047, 15183, 16555, 17787, 19160, 20376, 22004, 23517
Offset: 0

Views

Author

Robert Price, Apr 24 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. A246326.

Programs

  • Mathematica
    CAStep[rule_,a_]:=Map[rule[[10-#]]&,ListConvolve[{{0,2,0},{2,1,2},{0,2,0}},a,2],{2}];
code=454; 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 *)
Showing 1-10 of 12 results. Next

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

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