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A271412 Partial sums of the number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 358", based on the 5-celled von Neumann neighborhood. 1
1, 6, 10, 30, 39, 76, 100, 164, 189, 266, 335, 504, 548, 720, 824, 1096, 1180, 1416, 1596, 2008, 2176, 2584, 2792, 3312, 3553, 4094, 4466, 5318, 5694, 6622, 7035, 8044, 8560, 9776, 10296, 11584, 12104, 13336, 14005, 15526, 16271, 17988, 18736, 20516, 21429 (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=358; 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. A271409.

Sequence in context: A271134 A272087 A271261 * A272278 A272508 A218553

Adjacent sequences:  A271409 A271410 A271411 * A271413 A271414 A271415

KEYWORD

nonn,easy

AUTHOR

Robert Price, Apr 06 2016

STATUS

approved

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Last modified November 30 20:17 EST 2021. Contains 349425 sequences. (Running on oeis4.)