A267924 Decimal representation of the n-th iteration of the "Rule 245" elementary cellular automaton starting with a single ON (black) cell.

1, 3, 27, 123, 507, 2043, 8187, 32763, 131067, 524283, 2097147, 8388603, 33554427, 134217723, 536870907, 2147483643, 8589934587, 34359738363, 137438953467, 549755813883, 2199023255547, 8796093022203, 35184372088827, 140737488355323, 562949953421307

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 23 2016 and Apr 20 2019: (Start)

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

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

(End)

Empirical a(n) = 2^(2*n+1) - 5 for n>0. - Colin Barker, Nov 26 2016 and Apr 20 2019

Mathematica

rule=245; 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. A267922.

Sequence in context: A127210 A161807 A261716 * A241678 A063263 A204809

Adjacent sequences: A267921 A267922 A267923 * A267925 A267926 A267927

Keyword

nonn,easy

Author

Robert Price, Jan 22 2016

Status

approved