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

Author

Robert Price, Jan 21 2016

Keywords

• nonn

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

Crossrefs

Cf. A267848.

Programs

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 *)

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) = A002446(n) for n>1. - Colin Barker, Nov 26 2016