login
A266660
Binary representation of the n-th iteration of the "Rule 47" elementary cellular automaton starting with a single ON (black) cell.
2
1, 110, 11, 1111100, 11, 11111111100, 11, 111111111111100, 11, 1111111111111111100, 11, 11111111111111111111100, 11, 111111111111111111111111100, 11, 1111111111111111111111111111100, 11, 11111111111111111111111111111111100, 11
OFFSET
0,2
FORMULA
Conjectures from Colin Barker, Jan 03 2016 and Apr 18 2019: (Start)
a(n) = (199*(-1)^n+10^(2*n+1)-(-1)^n*10^(2*n+1)-1)/18 for n>1.
a(n) = 10001*a(n-2)-10000*a(n-4) for n>5.
G.f.: (1+110*x-9990*x^2+10990*x^3-100000*x^4+100000*x^5) / ((1-x)*(1+x)*(1-100*x)*(1+100*x)).
(End)
a(n) = A266254(n), n>1. - R. J. Mathar, Jan 10 2016
Conjecture: a(n) = (10*100^n - 100)/9 for odd n > 1; a(n) = 11 for even n > 1. - Karl V. Keller, Jr., Oct 10 2021
MATHEMATICA
rule=47; 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
KEYWORD
nonn,easy
AUTHOR
Robert Price, Jan 02 2016
STATUS
approved