login
A267351
Decimal representation of the n-th iteration of the "Rule 123" elementary cellular automaton starting with a single ON (black) cell.
2
1, 5, 14, 119, 56, 2015, 224, 32639, 896, 523775, 3584, 8386559, 14336, 134209535, 57344, 2147450879, 229376, 34359607295, 917504, 549755289599, 3670016, 8796090925055, 14680064, 140737479966719, 58720256, 2251799780130815, 234881024, 36028796884746239
OFFSET
0,2
FORMULA
Conjectures from Colin Barker, Jan 14 2016 and Apr 19 2019: (Start)
a(n) = 21*a(n-2)-84*a(n-4)+64*a(n-6) for n>6.
G.f.: (1+5*x-7*x^2+14*x^3-154*x^4-64*x^5+160*x^6) / ((1-x)*(1+x)*(1-2*x)*(1+2*x)*(1-4*x)*(1+4*x)).
(End)
MATHEMATICA
rule=123; 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: A316233 A317154 A283785 * A058072 A027304 A070135
KEYWORD
nonn,easy
AUTHOR
Robert Price, Jan 13 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