A269816 Partial sums of the number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 35", based on the 5-celled von Neumann neighborhood.

1, 6, 11, 48, 57, 158, 179, 364, 393, 706, 747, 1204, 1273, 1902, 2003, 2820, 2937, 4010, 4139, 5484, 5641, 7282, 7491, 9428, 9689, 11974, 12283, 14924, 15305, 18334, 18787, 22212, 22697, 26634, 27131, 31596, 32121, 37138, 37715, 43284, 43913, 50082, 50779

Offset

0,2

Comments

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

References

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

Links

Robert Price, Table of n, a(n) for n = 0..128

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=35; 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. A269814.

Sequence in context: A270899 A270327 A270932 * A270020 A269878 A292120

Adjacent sequences: A269813 A269814 A269815 * A269817 A269818 A269819

Keyword

nonn,easy

Author

Robert Price, Mar 05 2016

Status

approved