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A267451
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Number of ON (black) cells in the n-th iteration of the "Rule 131" elementary cellular automaton starting with a single ON (black) cell.
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1
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1, 1, 2, 2, 4, 3, 6, 5, 6, 7, 9, 7, 10, 10, 11, 11, 13, 12, 15, 14, 15, 16, 18, 16, 19, 19, 20, 20, 22, 21, 24, 23, 24, 25, 27, 25, 28, 28, 29, 29, 31, 30, 33, 32, 33, 34, 36, 34, 37, 37, 38, 38, 40, 39, 42, 41, 42, 43, 45, 43, 46, 46, 47, 47, 49, 48, 51, 50
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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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Conjectures from Colin Barker, Jan 15 2016 and Apr 19 2019: (Start)
a(n) = a(n-3)+a(n-4)-a(n-7) for n>6.
G.f.: (1+x+2*x^2+x^3+2*x^4+2*x^6) / ((1-x)^2*(1+x)*(1+x^2)*(1+x+x^2)).
(End)
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MATHEMATICA
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rule=131; 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
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AUTHOR
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STATUS
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approved
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