|
| |
|
|
A273571
|
|
Partial sums of the number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 798", based on the 5-celled von Neumann neighborhood.
|
|
1
|
|
|
|
1, 6, 19, 40, 77, 118, 203, 296, 421, 538, 747, 956, 1209, 1418, 1839, 2268, 2761, 3214, 3855, 4464, 5149, 5698, 6683, 7652, 8713, 9654, 10927, 12088, 13349, 14278, 16139, 18008, 20005, 21898, 24171, 26348, 28665, 30654, 33527, 36320, 39269, 41906, 45195
(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=798; 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. A273569.
Sequence in context: A273206 A273394 A273455 * A273778 A173980 A299281
Adjacent sequences: A273568 A273569 A273570 * A273572 A273573 A273574
|
|
|
KEYWORD
|
nonn,easy
|
|
|
AUTHOR
|
Robert Price, May 25 2016
|
|
|
STATUS
|
approved
|
| |
|
|
