A267360 Decimal representation of the n-th iteration of the "Rule 125" elementary cellular automaton starting with a single ON (black) cell.

1, 3, 28, 47, 496, 575, 8000, 9215, 128000, 147455, 2048000, 2359295, 32768000, 37748735, 524288000, 603979775, 8388608000, 9663676415, 134217728000, 154618822655, 2147483648000, 2473901162495, 34359738368000, 39582418599935, 549755813888000, 633318697598975

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) = 17*a(n-2)-16*a(n-4) for n>8.

G.f.: (1+3*x+11*x^2-4*x^3+36*x^4-176*x^5+16*x^6+192*x^7-64*x^8) / ((1-x)*(1+x)*(1-4*x)*(1+4*x)).

(End)

Mathematica

rule=125; 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. A267358, A267359.

Sequence in context: A157848 A225674 A253653 * A046104 A116984 A229055

Adjacent sequences: A267357 A267358 A267359 * A267361 A267362 A267363

Keyword

nonn,easy

Author

Robert Price, Jan 13 2016

Extensions

Removed an unjustified claim that Colin Barker's conjectures are correct. Removed a program based on a conjecture. - Michael De Vlieger, Jun 13 2022

Status

approved