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A273504 Partial sums of the number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 774", based on the 5-celled von Neumann neighborhood. 1
1, 6, 11, 28, 33, 58, 75, 136, 145, 190, 235, 360, 401, 558, 631, 852, 909, 1050, 1179, 1488, 1613, 1918, 2043, 2448, 2581, 3062, 3307, 3904, 4237, 4834, 5231, 6024, 6453, 7134, 7747, 8716, 9277, 10170, 10839, 11832, 12653, 13714, 14607, 15920, 16793, 18222 (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=774; 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. A273502.

Sequence in context: A061725 A105708 A253908 * A273608 A273681 A273705

Adjacent sequences:  A273501 A273502 A273503 * A273505 A273506 A273507

KEYWORD

nonn,easy

AUTHOR

Robert Price, May 23 2016

STATUS

approved

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Last modified February 23 06:00 EST 2020. Contains 332159 sequences. (Running on oeis4.)