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A267924
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Decimal representation of the n-th iteration of the "Rule 245" elementary cellular automaton starting with a single ON (black) cell.
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2
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1, 3, 27, 123, 507, 2043, 8187, 32763, 131067, 524283, 2097147, 8388603, 33554427, 134217723, 536870907, 2147483643, 8589934587, 34359738363, 137438953467, 549755813883, 2199023255547, 8796093022203, 35184372088827, 140737488355323, 562949953421307
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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 23 2016 and Apr 20 2019: (Start)
a(n) = 5*a(n-1)-4*a(n-2) for n>2.
G.f.: (1-2*x+16*x^2) / ((1-x)*(1-4*x)).
(End)
Empirical a(n) = 2^(2*n+1) - 5 for n>0. - Colin Barker, Nov 26 2016 and Apr 20 2019
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MATHEMATICA
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rule=245; 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,easy
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AUTHOR
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STATUS
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approved
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