|
|
A266792
|
|
Number of ON (black) cells in the n-th iteration of the "Rule 61" elementary cellular automaton starting with a single ON (black) cell.
|
|
1
|
|
|
1, 2, 2, 5, 4, 7, 5, 11, 5, 15, 5, 19, 5, 23, 5, 27, 5, 31, 5, 35, 5, 39, 5, 43, 5, 47, 5, 51, 5, 55, 5, 59, 5, 63, 5, 67, 5, 71, 5, 75, 5, 79, 5, 83, 5, 87, 5, 91, 5, 95, 5, 99, 5, 103, 5, 107, 5, 111, 5, 115, 5, 119, 5, 123, 5, 127, 5, 131, 5, 135, 5, 139
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
REFERENCES
|
S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
|
|
LINKS
|
|
|
FORMULA
|
Conjectures from Colin Barker, Jan 04 2016 and Apr 18 2019: (Start)
a(n) = n+1-(-1)^n*(n-4) for n>4.
a(n) = 2*a(n-2)-a(n-4) for n>8.
G.f.: (1+2*x+x^3+x^4-x^5-x^6+2*x^7-x^8) / ((1-x)^2*(1+x)^2).
(End)
|
|
MATHEMATICA
|
rule=61; rows=20; ca=CellularAutomaton[rule, {{1}, 0}, rows-1, {All, All}]; (* Start with single black cell *) catri=Table[Take[ca[[k]], {rows-k+1, rows+k-1}], {k, 1, rows}]; (* Truncated list of each row *) Table[Total[catri[[k]]], {k, 1, rows}] (* Number of Black cells in stage n *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|