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A271166 Partial sums of the number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 307", based on the 5-celled von Neumann neighborhood. 1
1, 6, 15, 47, 60, 164, 189, 381, 430, 746, 787, 1227, 1336, 1960, 2029, 2885, 3066, 4138, 4323, 5663, 5872, 7493, 7741, 9682, 10018, 12335, 12623, 15224, 15664, 18769, 19142, 22643, 23211, 27092, 27760, 32081, 32770, 37574, 38279, 43755, 44708, 50652, 51481 (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=307; 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. A271164.

Sequence in context: A244023 A271131 A271154 * A271248 A271399 A268154

Adjacent sequences:  A271163 A271164 A271165 * A271167 A271168 A271169

KEYWORD

nonn,easy

AUTHOR

Robert Price, Mar 31 2016

STATUS

approved

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Last modified May 9 19:47 EDT 2021. Contains 343746 sequences. (Running on oeis4.)