A269695 Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 6", based on the 5-celled von Neumann neighborhood.

1, 5, 4, 20, 4, 20, 16, 80, 4, 20, 16, 80, 16, 80, 64, 320, 4, 20, 16, 80, 16, 80, 64, 320, 16, 80, 64, 320, 64, 320, 256, 1280, 4, 20, 16, 80, 16, 80, 64, 320, 16, 80, 64, 320, 64, 320, 256, 1280, 16, 80, 64, 320, 64, 320, 256, 1280, 64, 320, 256, 1280, 256

Offset

0,2

Comments

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

Rules 38, 70, 102, 134, 166, 198 and 230 also generate this sequence.

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=6; 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: A133173 A307675 A266707 * A271065 A271598 A271133

Adjacent sequences: A269692 A269693 A269694 * A269696 A269697 A269698

Keyword

nonn,easy

Author

Robert Price, Mar 03 2016

Status

approved