[go: up one dir, main page]

login
A266752
Binary representation of the n-th iteration of the "Rule 163" elementary cellular automaton starting with a single ON (black) cell.
2
1, 100, 10010, 1001010, 100101010, 10010101010, 1001010101010, 100101010101010, 10010101010101010, 1001010101010101010, 100101010101010101010, 10010101010101010101010, 1001010101010101010101010, 100101010101010101010101010, 10010101010101010101010101010, 1001010101010101010101010101010
OFFSET
0,2
REFERENCES
S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
FORMULA
Conjectures from Colin Barker, Jan 20 2016 and Apr 18 2019: (Start)
a(n) = 101*a(n-1) - 100*a(n-2) for n>2.
G.f.: (1-x+10*x^2) / ((1-x)*(1-100*x)). (End)
Conjectured e.g.f.: (99 - 100*exp(x) + 991*exp(100*x))/990. - Stefano Spezia, Aug 05 2024
MATHEMATICA
rule=163; 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[FromDigits[catri[[k]]], {k, 1, rows}] (* binary representation of rows *)
CROSSREFS
Sequence in context: A045799 A096885 A267449 * A267523 A027576 A099374
KEYWORD
nonn,easy
AUTHOR
Robert Price, Jan 17 2016
STATUS
approved