A267294 Decimal representation of the n-th iteration of the "Rule 121" elementary cellular automaton starting with a single ON (black) cell.

1, 1, 26, 59, 476, 751, 7024, 16319, 115136, 195327, 1776384, 4177919, 29474816, 50003967, 454754304, 1069547519, 7545552896, 12801015807, 116417101824, 273804165119, 1931661541376, 3277060046847, 29802778066944, 70093866270719, 494505354592256

Offset

0,3

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 15 2016 and Apr 19 2019: (Start)

a(n) = a(n-2)+256*a(n-4)-256*a(n-6) for n>12.

G.f.: (1 +x +25*x^2 +58*x^3 +194*x^4 +436*x^5 +148*x^6 +720*x^7 -7088*x^8 +1856*x^9 -15040*x^10 -2816*x^11 +21760*x^12) / ((1-x)*(1+x)*(1-4*x)*(1+4*x)*(1+16*x^2)).

(End)

Mathematica

rule=121; 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. A267292.

Sequence in context: A038861 A277976 A291105 * A162316 A173085 A044128

Adjacent sequences: A267291 A267292 A267293 * A267295 A267296 A267297

Keyword

nonn,easy

Author

Robert Price, Jan 12 2016

Status

approved