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A271287 Partial sums of the number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 337", based on the 5-celled von Neumann neighborhood. 1
1, 5, 10, 50, 59, 159, 180, 380, 405, 729, 766, 1246, 1295, 1939, 2024, 2896, 2985, 4109, 4210, 5618, 5731, 7431, 7580, 9628, 9789, 12193, 12390, 15182, 15415, 18555, 18896, 22520, 22865, 26997, 27354, 32026, 32395, 37615, 38020, 43844, 44261, 50697, 51150 (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=337; 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. A271285.

Sequence in context: A336582 A271275 A270100 * A003587 A268100 A205884

Adjacent sequences:  A271284 A271285 A271286 * A271288 A271289 A271290

KEYWORD

nonn,easy

AUTHOR

Robert Price, Apr 03 2016

STATUS

approved

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Last modified May 9 13:42 EDT 2021. Contains 343742 sequences. (Running on oeis4.)