login
A267941
Decimal representation of the n-th iteration of the "Rule 253" elementary cellular automaton starting with a single ON (black) cell.
1
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.
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
KEYWORD
nonn,easy
AUTHOR
Robert Price, Jan 22 2016
STATUS
approved