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.

A269567 Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 622", based on the 5-celled von Neumann neighborhood.

Original entry on oeis.org

1, 6, 15, 36, 61, 98, 155, 224, 313, 414, 535, 668, 837, 1042, 1299, 1608, 1969, 2302, 2679, 3060, 3445, 3906, 4371, 4880, 5481, 6134, 6831, 7612, 8501, 9346, 10443, 11520, 12873, 14078, 15383, 16732, 18077, 19434, 20755, 22192, 23745, 25334, 26935, 28644
Offset: 0

Views

Author

Robert Price, Feb 29 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. A269522.

Programs

  • Mathematica
    rule=622; stages=300; ca=CellularAutomaton[ {rule,{2,{{0,2,0},{2,1,2},{0,2,0}}},{1,1}}, {{{1}},0}, stages]; (* Start with single black cell *) 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]}]

A269568 First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 622", based on the 5-celled von Neumann neighborhood.

Original entry on oeis.org

4, 4, 12, 4, 12, 20, 12, 20, 12, 20, 12, 36, 36, 52, 52, 52, -28, 44, 4, 4, 76, 4, 44, 92, 52, 44, 84, 108, -44, 252, -20, 276, -148, 100, 44, -4, 12, -36, 116, 116, 36, 12, 108, 20, 84, 124, 132, 292, -180, 212, -12, 132, 12, 300, 228, 52, 196, 148, 36, 276
Offset: 0

Views

Author

Robert Price, Feb 29 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. A269522.

Programs

  • Mathematica
    rule=622; stages=300; ca=CellularAutomaton[ {rule,{2,{{0,2,0},{2,1,2},{0,2,0}}},{1,1}}, {{{1}},0}, stages]; (* Start with single black cell *) on=Map[Function[Apply[Plus,Flatten[#1]]],ca]; (* Count ON cells at each stage *) Table[on[[i+1]]-on[[i]],{i,1,Length[on]-1}]

A269566 Number of active (ON, black) cells at stage 2^n-1 of the two-dimensional cellular automaton defined by "Rule 622", based on the 5-celled von Neumann neighborhood.

Original entry on oeis.org

1, 5, 21, 69, 309, 1077, 4661, 19173, 74917, 310285, 1234813, 4909789, 19434725, 76878941, 304281693, 1205650205
Offset: 0

Views

Author

Robert Price, Feb 29 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. A269522.

Programs

  • Mathematica
    rule=622; stages=300; ca=CellularAutomaton[ {rule,{2,{{0,2,0},{2,1,2},{0,2,0}}},{1,1}}, {{{1}},0}, stages]; (* Start with single black cell *) on=Map[Function[Apply[Plus,Flatten[#1]]],ca]; (* Count ON cells at each stage *) Part[on,2^Range[0,Log[2,stages]]]

Extensions

a(9)-a(15) from Lars Blomberg, Jul 16 2016
Showing 1-3 of 3 results.

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

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