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A267211
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Number of ON (black) cells in the n-th iteration of the "Rule 109" elementary cellular automaton starting with a single ON (black) cell.
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1
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1, 1, 5, 2, 7, 7, 10, 5, 13, 12, 13, 11, 18, 15, 19, 16, 21, 21, 24, 19, 27, 26, 27, 25, 32, 29, 33, 30, 35, 35, 38, 33, 41, 40, 41, 39, 46, 43, 47, 44, 49, 49, 52, 47, 55, 54, 55, 53, 60, 57, 61, 58, 63, 63, 66, 61, 69, 68, 69, 67, 74, 71, 75, 72, 77, 77
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OFFSET
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0,3
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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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a(n) = a(n-3)+a(n-4)-a(n-7) for n>7.
G.f.: (1+x+5*x^2+x^3+5*x^4+x^5+3*x^6-3*x^7) / ((1-x)^2*(1+x)*(1+x^2)*(1+x+x^2)).
(End)
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MATHEMATICA
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rule=109; 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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