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A266616
Number of OFF (white) cells in the n-th iteration of the "Rule 41" elementary cellular automaton starting with a single ON (black) cell.
1
0, 3, 3, 4, 8, 3, 11, 4, 16, 3, 19, 4, 24, 3, 27, 4, 32, 3, 35, 4, 40, 3, 43, 4, 48, 3, 51, 4, 56, 3, 59, 4, 64, 3, 67, 4, 72, 3, 75, 4, 80, 3, 83, 4, 88, 3, 91, 4, 96, 3, 99, 4, 104, 3, 107, 4, 112, 3, 115, 4, 120, 3, 123, 4, 128, 3, 131, 4, 136, 3, 139, 4
OFFSET
0,2
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.: x*(3+3*x+x^2+5*x^3-4*x^4) / ((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 *) nbc=Table[Total[catri[[k]]], {k, 1, rows}]; (* Number of Black cells in stage n *) Table[Length[catri[[k]]]-nbc[[k]], {k, 1, rows}] (* Number of White cells in stage n *)
CROSSREFS
Cf. A266608.
Sequence in context: A246023 A049927 A329216 * A360846 A340429 A147679
KEYWORD
nonn
AUTHOR
Robert Price, Jan 01 2016
STATUS
approved