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A267457
Decimal representation of the n-th iteration of the "Rule 133" elementary cellular automaton starting with a single ON (black) cell.
2
1, 2, 4, 8, 84, 168, 1364, 2728, 21844, 43688, 349524, 699048, 5592404, 11184808, 89478484, 178956968, 1431655764, 2863311528, 22906492244, 45812984488, 366503875924, 733007751848, 5864062014804, 11728124029608, 93824992236884, 187649984473768
OFFSET
0,2
FORMULA
Conjectures from Colin Barker, Jan 15 2016 and Apr 19 2019: (Start)
a(n) = 17*a(n-2)-16*a(n-4) for n>5.
G.f.: (1+2*x)*(1-13*x^2+32*x^4) / ((1-x)*(1+x)*(1-4*x)*(1+4*x)).
(End)
MATHEMATICA
rule=133; 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
Sequence in context: A018560 A087375 A018580 * A322614 A089337 A088114
KEYWORD
nonn,easy
AUTHOR
Robert Price, Jan 15 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