A269714 First differences of 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.

3, 4, 4, 8, 4, 20, -16, 24, 4, 48, -48, 48, 8, 100, -152, 56, 4, 112, -112, 112, 8, 224, -344, 112, 8, 224, -224, 224, 16, 452, -808, 120, 4, 240, -240, 240, 8, 480, -728, 240, 8, 480, -480, 480, 16, 960, -1704, 240, 8, 480, -480, 480, 16, 960, -1456, 480

Offset

0,1

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.

References

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

Links

Robert Price, Table of n, a(n) for n = 0..299

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 *)
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}] (* Difference at each stage *)

Crossrefs

Cf. A269711.

Sequence in context: A161496 A010612 A021033 * A146944 A294113 A339827

Adjacent sequences: A269711 A269712 A269713 * A269715 A269716 A269717

Keyword

sign,easy

Author

Robert Price, Mar 04 2016

Status

approved