A267274 Decimal representation of the n-th iteration of the "Rule 117" elementary cellular automaton starting with a single ON (black) cell.

1, 3, 24, 31, 384, 511, 6144, 8191, 98304, 131071, 1572864, 2097151, 25165824, 33554431, 402653184, 536870911, 6442450944, 8589934591, 103079215104, 137438953471, 1649267441664, 2199023255551, 26388279066624, 35184372088831, 422212465065984, 562949953421311

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 14 2016 and Apr 19 2019: (Start)

a(n) = ((-4)^n+(-1)^n+2^(2*n+1)-1)/2 for n>1.

a(n) = 17*a(n-2)-16*a(n-4) for n>5.

G.f.: (1+3*x+7*x^2-20*x^3-8*x^4+32*x^5) / ((1-x)*(1+x)*(1-4*x)*(1+4*x)).

(End)

Mathematica

rule=117; 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. A267272, A267273.

Sequence in context: A081312 A123598 A106217 * A217554 A278491 A363536

Adjacent sequences: A267271 A267272 A267273 * A267275 A267276 A267277

Keyword

nonn

Author

Robert Price, Jan 12 2016

Extensions

Removed an unjustified claim that Colin Barker's conjectures are correct. Removed a program based on a conjecture. - Michael De Vlieger, Jun 13 2022

Status

approved