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A266593
Number of ON (black) cells in the n-th iteration of the "Rule 37" elementary cellular automaton starting with a single ON (black) cell.
1
1, 1, 3, 2, 3, 6, 3, 10, 3, 14, 3, 18, 3, 22, 3, 26, 3, 30, 3, 34, 3, 38, 3, 42, 3, 46, 3, 50, 3, 54, 3, 58, 3, 62, 3, 66, 3, 70, 3, 74, 3, 78, 3, 82, 3, 86, 3, 90, 3, 94, 3, 98, 3, 102, 3, 106, 3, 110, 3, 114, 3, 118, 3, 122, 3, 126, 3, 130, 3, 134, 3, 138
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) = (-2*(-1)^n*n+2*n+7*(-1)^n-1)/2 for n>1.
a(n) = 2*a(n-2)-a(n-4) for n>5.
G.f.: (1+x+x^2-2*x^4+3*x^5) / ((1-x)^2*(1+x)^2).
(End)
MATHEMATICA
rule=37; 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. A266588.
Sequence in context: A240162 A113128 A220075 * A130459 A323621 A144216
KEYWORD
nonn,easy
AUTHOR
Robert Price, Jan 01 2016
STATUS
approved