login
A267622
Binary representation of the n-th iteration of the "Rule 187" elementary cellular automaton starting with a single ON (black) cell.
1
1, 101, 10111, 1011111, 101111111, 10111111111, 1011111111111, 101111111111111, 10111111111111111, 1011111111111111111, 101111111111111111111, 10111111111111111111111, 1011111111111111111111111, 101111111111111111111111111, 10111111111111111111111111111
OFFSET
0,2
REFERENCES
S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
FORMULA
Conjectures from Colin Barker, Jan 19 2016 and Apr 20 2019: (Start)
a(n) = 101*a(n-1)-100*a(n-2) for n>2.
G.f.: (1+10*x^2) / ((1-x)*(1-100*x)).
(End)
MATHEMATICA
rule=187; 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: A065074 A113628 A135375 * A172162 A096884 A055474
KEYWORD
nonn,easy
AUTHOR
Robert Price, Jan 18 2016
STATUS
approved