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A270722 Partial sums of the number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 201", based on the 5-celled von Neumann neighborhood. 1
1, 5, 14, 42, 59, 139, 167, 300, 364, 605, 677, 1025, 1134, 1666, 1803, 2459, 2671, 3536, 3740, 4789, 5085, 6434, 6738, 8295, 8727, 10508, 11004, 13089, 13721, 16142, 16862, 19567, 20311, 23416, 24328, 27832, 28681, 32713, 33873, 38222, 39350, 44254, 45487 (list; graph; refs; listen; history; text; internal format)
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

CAStep[rule_, a_]:=Map[rule[[10-#]]&, ListConvolve[{{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}, a, 2], {2}];

code=201; stages=128;

rule=IntegerDigits[code, 2, 10];

g=2*stages+1; (* Maximum size of grid *)

a=PadLeft[{{1}}, {g, g}, 0, Floor[{g, g}/2]]; (* Initial ON cell on grid *)

ca=a;

ca=Table[ca=CAStep[rule, ca], {n, 1, stages+1}];

PrependTo[ca, a];

(* Trim full grid to reflect growth by one cell at each stage *)

k=(Length[ca[[1]]]+1)/2;

ca=Table[Table[Part[ca[[n]][[j]], Range[k+1-n, k-1+n]], {j, k+1-n, k-1+n}], {n, 1, k}];

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. A270720.

Sequence in context: A198086 A272018 A272091 * A272282 A270893 A272316

Adjacent sequences:  A270719 A270720 A270721 * A270723 A270724 A270725

KEYWORD

nonn,easy

AUTHOR

Robert Price, Mar 22 2016

STATUS

approved

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Last modified January 21 05:35 EST 2021. Contains 340333 sequences. (Running on oeis4.)