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A267678
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Decimal representation of the n-th iteration of the "Rule 197" elementary cellular automaton starting with a single ON (black) cell.
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2
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1, 2, 20, 104, 468, 1960, 8020, 32424, 130388, 522920, 2094420, 8383144, 33543508, 134195880, 536827220, 2147396264, 8589759828, 34359388840, 137438254420, 549754415784, 2199020459348, 8796087429800, 35184360904020, 140737465985704, 562949908682068
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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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a(n) = 6*a(n-1)-7*a(n-2)-6*a(n-3)+8*a(n-4) for n>5.
G.f.: (1-4*x+15*x^2+4*x^3-12*x^4-16*x^5) / ((1-x)*(1+x)*(1-2*x)*(1-4*x)).
(End)
Conjecture: a(n) = 2*(-3 + (-1)^n - 2^(2+n) + 3*4^n)/3 for n>1. - Colin Barker, Feb 14 2017
Conjecture: a(n) = floor((6*4^n - 8*2^n)/3) - 2^(n mod 2) for n > 1. - Karl V. Keller, Jr., Jun 01 2022
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MATHEMATICA
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rule=197; 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[FromDigits[catri[[k]], 2], {k, 1, rows}] (* Decimal Representation of Rows *)
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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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