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A267046
Number of ON (black) cells in the n-th iteration of the "Rule 91" elementary cellular automaton starting with a single ON (black) cell.
1
1, 2, 2, 4, 5, 8, 5, 12, 5, 16, 5, 20, 5, 24, 5, 28, 5, 32, 5, 36, 5, 40, 5, 44, 5, 48, 5, 52, 5, 56, 5, 60, 5, 64, 5, 68, 5, 72, 5, 76, 5, 80, 5, 84, 5, 88, 5, 92, 5, 96, 5, 100, 5, 104, 5, 108, 5, 112, 5, 116, 5, 120, 5, 124, 5, 128, 5, 132, 5, 136, 5, 140
OFFSET
0,2
REFERENCES
S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
FORMULA
Conjectures from Colin Barker, Jan 10 2016 and Apr 19 2019: (Start)
a(n) = 3/2+(7*(-1)^n)/2+n-(-1)^n*n for n>2.
a(n) = 2*a(n-2)-a(n-4) for n>6.
G.f.: (1+2*x+2*x^4+2*x^5-3*x^6) / ((1-x)^2*(1+x)^2).
(End)
MATHEMATICA
rule=91; 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. A267015.
Sequence in context: A292382 A296561 A300121 * A308902 A166515 A339560
KEYWORD
nonn,easy
AUTHOR
Robert Price, Jan 09 2016
STATUS
approved