A269697 Partial sums of the 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, 6, 10, 30, 34, 54, 70, 150, 154, 174, 190, 270, 286, 366, 430, 750, 754, 774, 790, 870, 886, 966, 1030, 1350, 1366, 1446, 1510, 1830, 1894, 2214, 2470, 3750, 3754, 3774, 3790, 3870, 3886, 3966, 4030, 4350, 4366, 4446, 4510, 4830, 4894, 5214, 5470, 6750

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

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

Crossrefs

Cf. A269695.

Sequence in context: A103767 A025129 A093559 * A271067 A271600 A271134

Adjacent sequences: A269694 A269695 A269696 * A269698 A269699 A269700

Keyword

nonn,easy

Author

Robert Price, Mar 03 2016

Status

approved