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

Author

Robert Price, Mar 03 2016

Keywords

• nonn
• easy

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

Programs

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 *)