A267847 Decimal representation of the n-th iteration of the "Rule 227" elementary cellular automaton starting with a single ON (black) cell.

1, 4, 26, 122, 506, 2042, 8186, 32762, 131066, 524282, 2097146, 8388602, 33554426, 134217722, 536870906, 2147483642, 8589934586, 34359738362, 137438953466, 549755813882, 2199023255546, 8796093022202, 35184372088826, 140737488355322, 562949953421306

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-x+10*x^2+8*x^3) / ((1-x)*(1-4*x)).

(End)

Conjecture: a(n) = 2*(4^n - 3) for n>1. - Colin Barker, Nov 26 2016

Mathematica

rule=227; 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. A267845.

Sequence in context: A140804 A147621 A246854 * A211166 A245460 A261738

Adjacent sequences: A267844 A267845 A267846 * A267848 A267849 A267850

Keyword

nonn

Author

Robert Price, Jan 21 2016

Status

approved