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A266220
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Number of ON (black) cells in the n-th iteration of the "Rule 7" elementary cellular automaton starting with a single ON (black) cell.
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2
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1, 2, 0, 7, 0, 11, 0, 15, 0, 19, 0, 23, 0, 27, 0, 31, 0, 35, 0, 39, 0, 43, 0, 47, 0, 51, 0, 55, 0, 59, 0, 63, 0, 67, 0, 71, 0, 75, 0, 79, 0, 83, 0, 87, 0, 91, 0, 95, 0, 99, 0, 103, 0, 107, 0, 111, 0, 115, 0, 119, 0, 123, 0, 127, 0, 131, 0, 135, 0, 139, 0
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OFFSET
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0,2
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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, Dec 25 2015 and Apr 13 2019: (Start)
a(n) = 1/2*(1-(-1)^n)*(2*n+1) for n>1.
a(n) = 2*a(n-2) - a(n-4) for n>5.
G.f.: (1+2*x-2*x^2+3*x^3+x^4-x^5) / ((1-x)^2*(1+x)^2).
(End)
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MATHEMATICA
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rule=7; 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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