A267042 Decimal representation of the n-th iteration of the "Rule 91" elementary cellular automaton starting with a single ON (black) cell.

1, 5, 10, 99, 124, 1935, 496, 32319, 1984, 522495, 7936, 8381439, 31744, 134189055, 126976, 2147368959, 507904, 34359279615, 2031616, 549753978879, 8126464, 8796085682175, 32505856, 140737458995199, 130023424, 2251799696244735, 520093696, 36028796549201919

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 10 2016: (Start)

a(n) = 21*a(n-2)-84*a(n-4)+64*a(n-6) for n>8.

G.f.: (1+5*x-11*x^2-6*x^3-2*x^4+276*x^5-1332*x^6-320*x^7+1344*x^8) / ((1-x)*(1+x)*(1-2*x)*(1+2*x)*(1-4*x)*(1+4*x)).

(End)

Mathematica

rule=91; 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. A267015, A267041.

Sequence in context: A120598 A200983 A344140 * A119137 A048360 A357565

Adjacent sequences: A267039 A267040 A267041 * A267043 A267044 A267045

Keyword

nonn

Author

Robert Price, Jan 09 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