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 16 results. Next

A169700 First differences of A169699.

Original entry on oeis.org

4, 7, 13, 3, 28, 0, 57, -53, 60, 0, 120, -120, 120, 0, 241, -357, 124, 0, 248, -248, 248, 0, 496, -744, 248, 0, 496, -496, 496, 0, 993, -1733, 252, 0, 504, -504, 504, 0, 1008, -1512, 504, 0, 1008, -1008, 1008, 0, 2016, -3528, 504, 0, 1008, -1008, 1008, 0, 2016, -3024, 1008, 0, 2016, -2016
Offset: 0

Views

Author

N. J. A. Sloane, Apr 17 2010

Keywords

Links

A246316 Total number of ON cells at stage n of two-dimensional 5-neighbor outer totalistic cellular automaton defined by "Rule 452".

Original entry on oeis.org

1, 4, 5, 12, 8, 24, 25, 40, 33, 44, 40, 88, 77, 100, 121, 176, 137, 164, 141, 204, 217, 288, 309, 384, 353, 404, 401, 508, 513, 564, 601, 724, 701, 672, 729, 824, 849, 964, 981, 1168, 1129, 1124, 1113, 1268, 1341, 1424, 1497, 1644, 1625, 1664, 1653, 1856, 1869, 2016, 2037, 2256, 2221, 2316, 2329, 2548, 2589, 2924
Offset: 0

Views

Author

N. J. A. Sloane, Aug 27 2014

Keywords

Comments

Also "Rule 460".
Rules that produce this sequence: 324, 332, 356, 364, 452, 460, 484, 492, 836, 844, 868, 876, 964, 972, 996, 1004. - Robert Price, Apr 02 2016

References

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

Links

Crossrefs

Cf. A169699, A246317.

Programs

  • Mathematica
    Map[Function[Apply[Plus, Flatten[ #1]]], CellularAutomaton[{ 452, {2, {{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}}, {1, 1}}, {{{1}}, 0}, 130]]
ArrayPlot /@ CellularAutomaton[{452, {2, {{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}}, {1, 1}}, {{{1}}, 0}, 23]

A246326 Total number of ON cells at stage n of two-dimensional 5-neighbor outer totalistic cellular automaton defined by "Rule 454".

Original entry on oeis.org

1, 5, 4, 20, 9, 37, 28, 57, 29, 72, 72, 145, 97, 165, 157, 233, 141, 249, 205, 289, 269, 433, 428, 504, 337, 488, 448, 709, 561, 705, 708, 980, 733, 896, 892, 924, 876, 1141, 1136, 1372, 1232, 1373, 1216, 1628, 1513, 1857, 1637, 1992, 1684, 2136, 2089, 2260, 2168, 2428, 2505, 2700, 2508, 2812, 2649, 2945, 2900, 3216, 3328
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.

Programs

  • Mathematica
    Map[Function[Apply[Plus, Flatten[ #1]]], CellularAutomaton[{ 454, {2, {{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}}, {1, 1}}, {{{1}}, 0}, 130]]
ArrayPlot /@ CellularAutomaton[{454, {2, {{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}}, {1, 1}}, {{{1}}, 0}, 23]

A246318 Total number of ON cells at stage 2n of two-dimensional 5-neighbor outer totalistic cellular automaton defined by "Rule 451".

Original entry on oeis.org

1, 9, 21, 45, 93, 117, 173, 205, 293, 225, 145, 369, 609, 597, 661, 789, 1033, 845, 685, 1157, 1185, 1245, 1629, 1669, 1601, 1881, 1857, 1957, 2485, 2885, 2565, 2497, 3541, 3113, 2561, 3401, 3393, 3633, 3801, 4505, 4189, 4049, 4941, 5717, 5197, 5861, 6337, 6105, 7085, 6640, 6212, 7280, 7408, 7580
Offset: 0

Views

Author

N. J. A. Sloane, Aug 27 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.

Programs

  • Mathematica
    Map[Function[Apply[Plus, Flatten[ #1]]], CellularAutomaton[{ 451, {2, {{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}}, {1, 1}}, {{{1}}, 0}, 130]] (* then take every other term *)
ArrayPlot /@ CellularAutomaton[{451, {2, {{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}}, {1, 1}}, {{{1}}, 0}, 23]

A246325 Total number of ON cells at stage 2n of two-dimensional 5-neighbor outer totalistic cellular automaton defined by "Rule 453".

Original entry on oeis.org

1, 5, 17, 29, 49, 61, 93, 149, 117, 197, 237, 229, 285, 297, 409, 441, 537, 485, 677, 733, 865, 793, 881, 877, 1097, 1301, 1233, 1529, 1461, 1533, 1633, 1869, 1881, 2149, 2185, 2393, 2677, 2801, 2681, 2881, 2921, 3089, 3193, 3521, 3561, 4041, 4137, 3985, 4161, 4417, 4433, 4601, 4865, 4981, 5041, 5381, 5917, 5897, 6209, 6453, 6337, 6593, 7293, 7049, 7493
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.

Programs

  • Mathematica
    Map[Function[Apply[Plus, Flatten[ #1]]], CellularAutomaton[{ 453, {2, {{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}}, {1, 1}}, {{{1}}, 0}, 130]] (* then take every other term *)
ArrayPlot /@ CellularAutomaton[{453, {2, {{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}}, {1, 1}}, {{{1}}, 0}, 23]

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]

A253089 Number of ON cells at generation n of 9-celled totalistic CA defined by Rule 510.

Original entry on oeis.org

1, 9, 20, 29, 69, 44, 112, 84, 228, 81, 253, 240, 361, 329, 408, 436, 552, 544, 656, 852, 748, 752, 1040, 1173, 1097, 928, 1389, 1857, 1208, 1244, 1664, 2457, 1448, 1636, 2028, 2732, 2164, 1957, 2841, 3204, 2849, 2301, 3504, 3869, 3548, 2756, 4140, 4509, 4060, 3388
Offset: 0

Views

Author

N. J. A. Sloane, Feb 12 2015

Keywords

Links

Crossrefs

Cf. A169699 (5-neighbor analog).

Programs

  • Mathematica
    Map[Function[Apply[Plus, Flatten[#1]]],
CellularAutomaton[{510, {2, {{2, 2, 2}, {2, 1, 2}, {2, 2, 2}}}, {1, 1}}, {{{1}}, 0}, 66]]
ArrayPlot /@ CellularAutomaton[{510, {2, {{2, 2, 2}, {2, 1, 2}, {2, 2, 2}}}, {1, 1}}, {{{1}}, 0}, 15]

Formula

It would be nice to have a recurrence.

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]
Showing 1-10 of 16 results. Next

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

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