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A266981
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Number of ON (black) cells in the n-th iteration of the "Rule 79" elementary cellular automaton starting with a single ON (black) cell.
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1
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1, 2, 2, 5, 3, 8, 4, 11, 5, 14, 6, 17, 7, 20, 8, 23, 9, 26, 10, 29, 11, 32, 12, 35, 13, 38, 14, 41, 15, 44, 16, 47, 17, 50, 18, 53, 19, 56, 20, 59, 21, 62, 22, 65, 23, 68, 24, 71, 25, 74, 26, 77, 27, 80, 28, 83, 29, 86, 30, 89, 31, 92, 32, 95, 33, 98, 34
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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, Jan 08 2016 and Apr 19 2019: (Start)
a(n) = (3+(-1)^n-2*(-2+(-1)^n)*n)/4.
a(n) = 2*a(n-2)-a(n-4) for n>3.
G.f.: (1+2*x+x^3) / ((1-x)^2*(1+x)^2).
(End)
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MATHEMATICA
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rule=79; 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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