A267921 Decimal representation of the n-th iteration of the "Rule 243" elementary cellular automaton starting with a single ON (black) cell.

1, 5, 29, 125, 509, 2045, 8189, 32765, 131069, 524285, 2097149, 8388605, 33554429, 134217725, 536870909, 2147483645, 8589934589, 34359738365, 137438953469, 549755813885, 2199023255549, 8796093022205, 35184372088829, 140737488355325, 562949953421309

Offset: 0

Author

Robert Price, Jan 22 2016

Keywords

• nonn
• easy

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. A267919.

Programs

Mathematica

rule=243; 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 22 2016 and Apr 16 2019: (Start)

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

G.f.: (1+8*x^2) / ((1-x)*(1-4*x)).

(End)

Empirical a(n) = 2^(2*n+1) - 3 for n>0. - Colin Barker, Nov 25 2016