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A273024 Partial sums of the number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 577", based on the 5-celled von Neumann neighborhood. 1
1, 5, 22, 47, 99, 172, 285, 405, 618, 831, 1131, 1416, 1896, 2381, 2922, 3486, 4231, 5008, 5916, 6837, 8021, 9225, 10562, 11895, 13579, 15256, 17133, 19045, 21286, 23511, 25900, 28497, 31297, 34190, 37375, 40483, 44216, 47837, 51645, 55730, 60303, 64643 (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=577; 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. A273022.

Sequence in context: A290510 A184724 A082005 * A273121 A099078 A272836

Adjacent sequences:  A273021 A273022 A273023 * A273025 A273026 A273027

KEYWORD

nonn,easy

AUTHOR

Robert Price, May 13 2016

STATUS

approved

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Last modified July 1 08:17 EDT 2022. Contains 354953 sequences. (Running on oeis4.)