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A272811 Partial sums of the number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 542", based on the 5-celled von Neumann neighborhood. 1
1, 6, 19, 40, 73, 110, 179, 232, 349, 430, 583, 684, 909, 1046, 1327, 1500, 1865, 2098, 2543, 2836, 3377, 3778, 4463, 4880, 5689, 6150, 7007, 7644, 8557, 9402, 10427, 11292, 12485, 13514, 14915, 16012, 17501, 18814, 20443, 21868, 23689, 25290, 27387, 28992 (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=542; 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. A272809.

Sequence in context: A179986 A054567 A096957 * A273206 A273394 A273455

Adjacent sequences:  A272808 A272809 A272810 * A272812 A272813 A272814

KEYWORD

nonn,easy

AUTHOR

Robert Price, May 06 2016

STATUS

approved

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Last modified June 23 21:09 EDT 2021. Contains 345402 sequences. (Running on oeis4.)