login
A266614
Number of ON (black) cells in the n-th iteration of the "Rule 41" elementary cellular automaton starting with a single ON (black) cell.
1
1, 0, 2, 3, 1, 8, 2, 11, 1, 16, 2, 19, 1, 24, 2, 27, 1, 32, 2, 35, 1, 40, 2, 43, 1, 48, 2, 51, 1, 56, 2, 59, 1, 64, 2, 67, 1, 72, 2, 75, 1, 80, 2, 83, 1, 88, 2, 91, 1, 96, 2, 99, 1, 104, 2, 107, 1, 112, 2, 115, 1, 120, 2, 123, 1, 128, 2, 131, 1, 136, 2, 139
OFFSET
0,3
REFERENCES
S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
FORMULA
Conjectures from Colin Barker, Jan 02 2016 and Apr 18 2019: (Start)
a(n) = a(n-2)+a(n-4)-a(n-6) for n>5.
G.f.: (1+x^2+3*x^3-2*x^4+5*x^5) / ((1-x)^2*(1+x)^2*(1+x^2)).
(End)
MATHEMATICA
rule=41; 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[Total[catri[[k]]], {k, 1, rows}] (* Number of Black cells in stage n *)
CROSSREFS
Cf. A266608.
Sequence in context: A109198 A081320 A147865 * A175314 A331123 A182223
KEYWORD
nonn,easy
AUTHOR
Robert Price, Jan 01 2016
STATUS
approved