login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A273326 Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 646", based on the 5-celled von Neumann neighborhood. 4
1, 5, 5, 17, 9, 29, 17, 61, 17, 77, 33, 125, 45, 161, 69, 257, 61, 281, 85, 353, 97, 389, 121, 485, 121, 533, 169, 677, 205, 785, 277, 1073, 245, 1121, 293, 1265, 305, 1301, 329, 1397, 329, 1445, 377, 1589, 413, 1697, 485, 1985, 461, 2057, 533, 2273, 569 (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

Robert Price, Diagrams of the first 20 stages

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=646; 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}];

Map[Function[Apply[Plus, Flatten[#1]]], ca] (* Count ON cells at each stage *)

CROSSREFS

Sequence in context: A294612 A246332 A300784 * A273421 A273758 A273835

Adjacent sequences:  A273323 A273324 A273325 * A273327 A273328 A273329

KEYWORD

nonn,easy

AUTHOR

Robert Price, May 20 2016

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 11 06:25 EDT 2020. Contains 336422 sequences. (Running on oeis4.)