A267935 Decimal representation of the n-th iteration of the "Rule 249" elementary cellular automaton starting with a single ON (black) cell.

1, 1, 27, 127, 511, 2047, 8191, 32767, 131071, 524287, 2097151, 8388607, 33554431, 134217727, 536870911, 2147483647, 8589934591, 34359738367, 137438953471, 549755813887, 2199023255551, 8796093022207, 35184372088831, 140737488355327, 562949953421311

Offset

0,3

References

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

Links

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

Eric Weisstein's World of Mathematics, Elementary Cellular Automaton

S. Wolfram, A New Kind of Science

Index entries for sequences related to cellular automata

Index to Elementary Cellular Automata

Formula

Conjectures from Colin Barker, Jan 23 2016 and Apr 20 2019: (Start)

a(n) = 5*a(n-1)-4*a(n-2) for n>4.

G.f.: (1-4*x+26*x^2-4*x^3-16*x^4) / ((1-x)*(1-4*x)).

(End)

Empirical a(n) = 2^(2*n+1) - 1 for n>2. - Colin Barker, Nov 26 2016 and Apr 20 2019

Mathematica

rule=249; 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. A267927.

Sequence in context: A044359 A044740 A026917 * A048615 A124955 A126414

Adjacent sequences: A267932 A267933 A267934 * A267936 A267937 A267938

Keyword

nonn,easy

Author

Robert Price, Jan 22 2016

Status

approved