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A271131 Partial sums of the number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 291", based on the 5-celled von Neumann neighborhood. 1
1, 6, 15, 47, 56, 157, 198, 362, 395, 711, 772, 1205, 1258, 1858, 1999, 2824, 2900, 3997, 4157, 5442, 5534, 7163, 7431, 9240, 9513, 11838, 12090, 14679, 14943, 17832, 18253, 21602, 21998, 25807, 26247, 30456, 30849, 35642, 36307, 41431, 41984, 47976, 48625 (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=291; 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. A271129.

Sequence in context: A215917 A082637 A244023 * A271154 A271166 A271248

Adjacent sequences:  A271128 A271129 A271130 * A271132 A271133 A271134

KEYWORD

nonn,easy

AUTHOR

Robert Price, Mar 31 2016

STATUS

approved

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Last modified February 16 21:46 EST 2020. Contains 331975 sequences. (Running on oeis4.)