A267851 Decimal representation of the n-th iteration of the "Rule 229" elementary cellular automaton starting with a single ON (black) cell.

1, 2, 30, 126, 510, 2046, 8190, 32766, 131070, 524286, 2097150, 8388606, 33554430, 134217726, 536870910, 2147483646, 8589934590, 34359738366, 137438953470, 549755813886, 2199023255550, 8796093022206, 35184372088830, 140737488355326, 562949953421310

Offset

0,2

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 21 2016: (Start)

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

G.f.: (1-3*x+24*x^2-16*x^3) / ((1-x)*(1-4*x)).

(End)

Conjecture: a(n) = 2*(4^n - 1) for n>1. - Colin Barker, Nov 26 2016

Mathematica

rule=229; 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. A267848.

Sequence in context: A157870 A285991 A078838 * A089288 A232602 A154413

Adjacent sequences: A267848 A267849 A267850 * A267852 A267853 A267854

Keyword

nonn

Author

Robert Price, Jan 21 2016

Status

approved