A267271 Decimal representation of the n-th iteration of the "Rule 115" elementary cellular automaton starting with a single ON (black) cell.

1, 5, 12, 111, 96, 1919, 768, 31743, 6144, 516095, 49152, 8323071, 393216, 133693439, 3145728, 2143289343, 25165824, 34326183935, 201326592, 549487378431, 1610612736, 8793945538559, 12884901888, 140720308486143, 103079215104, 2251662374731775, 824633720832

Offset

0,2

Links

Robert Price, Table of n, a(n) for n = 0..1000

Eric Weisstein's World of Mathematics, Elementary Cellular Automaton

Stephen Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.

Index entries for sequences related to cellular automata

Index to Elementary Cellular Automata

Formula

Conjectures from Colin Barker, Jan 14 2016 and Apr 19 2019: (Start)

a(n) = 25*a(n-2) - 152*a(n-4) + 128*a(n-6) for n > 6.

G.f.: (1 + 5*x - 13*x^2 - 14*x^3 - 52*x^4 - 96*x^5 + 64*x^6) / ((1-x)*(1+x)*(1-4*x)*(1+4*x)*(1-8*x^2)).

(End)

Mathematica

rule=115; 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]], 2], {k, 1, rows}]   (* decimal representation of rows *)

Crossrefs

Cf. A267269, A267270.

Sequence in context: A304001 A009731 A009427 * A009754 A096314 A332466

Adjacent sequences: A267268 A267269 A267270 * A267272 A267273 A267274

Keyword

nonn,easy

Author

Robert Price, Jan 12 2016

Status

approved