|
|
A267360
|
|
Decimal representation of the n-th iteration of the "Rule 125" elementary cellular automaton starting with a single ON (black) cell.
|
|
2
|
|
|
1, 3, 28, 47, 496, 575, 8000, 9215, 128000, 147455, 2048000, 2359295, 32768000, 37748735, 524288000, 603979775, 8388608000, 9663676415, 134217728000, 154618822655, 2147483648000, 2473901162495, 34359738368000, 39582418599935, 549755813888000, 633318697598975
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
LINKS
|
|
|
FORMULA
|
Conjectures from Colin Barker, Jan 14 2016 and Apr 19 2019: (Start)
a(n) = 17*a(n-2)-16*a(n-4) for n>8.
G.f.: (1+3*x+11*x^2-4*x^3+36*x^4-176*x^5+16*x^6+192*x^7-64*x^8) / ((1-x)*(1+x)*(1-4*x)*(1+4*x)).
(End)
|
|
MATHEMATICA
|
rule=125; 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
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|