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A267872
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Number of ON (black) cells in the n-th iteration of the "Rule 237" elementary cellular automaton starting with a single ON (black) cell.
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1
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1, 1, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 117, 119, 121, 123, 125
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OFFSET
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0,3
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COMMENTS
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REFERENCES
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S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
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LINKS
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FORMULA
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Conjectures from Colin Barker, Jan 22 2016 and Apr 20 2019: (Start)
a(n) = 2*a(n-1)-a(n-2) for n>3.
G.f.: (1-x+4*x^2-2*x^3) / (1-x)^2.
(End)
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MATHEMATICA
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rule=237; 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 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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