A267941 Decimal representation of the n-th iteration of the "Rule 253" elementary cellular automaton starting with a single ON (black) cell.

1, 3, 31, 127, 511, 2047, 8191, 32767, 131071, 524287, 2097151, 8388607, 33554431, 134217727, 536870911, 2147483647, 8589934591, 34359738367, 137438953471, 549755813887, 2199023255551, 8796093022207, 35184372088831, 140737488355327, 562949953421311

Offset

0,2

Comments

With the exception of a(1) the same as A267938, A267890, A267888 and A083420. - R. J. Mathar, Jan 24 2016

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 16 2019: (Start)

a(n) = 5*a(n-1)-4*a(n-2) for n>3.

G.f.: (1-2*x+20*x^2-16*x^3) / ((1-x)*(1-4*x)).

(End)

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

Mathematica

rule=253; 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. A060576.

Sequence in context: A199367 A295534 A119682 * A069630 A069615 A087389

Adjacent sequences: A267938 A267939 A267940 * A267942 A267943 A267944

Keyword

nonn,easy

Author

Robert Price, Jan 22 2016

Status

approved