A269711 Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 20", based on the 5-celled von Neumann neighborhood.

1, 4, 8, 12, 20, 24, 44, 28, 52, 56, 104, 56, 104, 112, 212, 60, 116, 120, 232, 120, 232, 240, 464, 120, 232, 240, 464, 240, 464, 480, 932, 124, 244, 248, 488, 248, 488, 496, 976, 248, 488, 496, 976, 496, 976, 992, 1952, 248, 488, 496, 976, 496, 976, 992

Offset

0,2

Comments

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

Rules 28, 52, 60, 148, 156, 180, 188, 532, 540, 564, 572, 660, 668, 692 and 700 also generate this sequence.

Apparently a duplicate of A122108. - R. J. Mathar, Mar 09 2016

References

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

Links

Robert Price, Table of n, a(n) for n = 0..300

Robert Price, Diagrams of first 20 stages.

N. J. A. Sloane, On the Number of ON Cells in Cellular Automata, arXiv:1503.01168 [math.CO], 2015.

Eric Weisstein's World of Mathematics, Elementary Cellular Automaton

S. Wolfram, A New Kind of Science

Index entries for sequences related to cellular automata

Index to 2D 5-Neighbor Cellular Automata

Index to Elementary Cellular Automata

Mathematica

rule=20; 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 *)
Map[Function[Apply[Plus, Flatten[#1]]], ca] (* Count ON cells at each stage *)

Crossrefs

Sequence in context: A090658 A268799 A359955 * A122108 A311658 A311659

Adjacent sequences: A269708 A269709 A269710 * A269712 A269713 A269714

Keyword

nonn,easy

Author

Robert Price, Mar 04 2016

Status

approved