|
|
A267528
|
|
Number of ON (black) cells in the n-th iteration of the "Rule 141" elementary cellular automaton starting with a single ON (black) cell.
|
|
2
|
|
|
1, 1, 2, 3, 5, 6, 8, 9, 11, 12, 14, 15, 17, 18, 20, 21, 23, 24, 26, 27, 29, 30, 32, 33, 35, 36, 38, 39, 41, 42, 44, 45, 47, 48, 50, 51, 53, 54, 56, 57, 59, 60, 62, 63, 65, 66, 68, 69, 71, 72, 74, 75, 77, 78, 80, 81, 83, 84, 86, 87, 89, 90, 92, 93, 95, 96, 98
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
REFERENCES
|
S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
|
|
LINKS
|
|
|
FORMULA
|
Conjectures from Colin Barker, Jan 16 2016 and Apr 17 2019: (Start)
a(n) = a(n-1) + a(n-2) - a(n-3) for n > 4.
G.f.: (1 + x^3 + x^4)/((1 - x)^2*(1 + x)). (End)
Conjectured e.g.f.: 2 + x + (3*x/2 - 1)*cosh(x) + 3*(x - 1)*sinh(x)/2. - Stefano Spezia, Feb 20 2023
|
|
MATHEMATICA
|
rule=141; 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
|
|
|
|