A269709 Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 14", based on the 5-celled von Neumann neighborhood.

1, 6, 14, 34, 54, 86, 126, 202, 270, 350, 438, 562, 686, 846, 1030, 1322, 1582, 1854, 2134, 2450, 2766, 3118, 3494, 3978, 4438, 4934, 5454, 6082, 6710, 7446, 8254, 9386, 10414, 11454, 12502, 13586, 14670, 15790, 16934, 18186, 19414, 20678, 21966, 23362

Offset

0,2

Comments

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

Rules 46, 142 and 174 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=14; 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. A269707.

Sequence in context: A279730 A269717 A271097 * A270093 A270735 A270170

Adjacent sequences: A269706 A269707 A269708 * A269710 A269711 A269712

Keyword

nonn,easy

Author

Robert Price, Mar 04 2016

Status

approved