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A267527
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Decimal representation of the n-th iteration of the "Rule 141" elementary cellular automaton starting with a single ON (black) cell.
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2
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1, 2, 5, 11, 87, 175, 1375, 2751, 21887, 43775, 349695, 699391, 5593087, 11186175, 89481215, 178962431, 1431666687, 2863333375, 22906535935, 45813071871, 366504050687, 733008101375, 5864062713855, 11728125427711, 93824995033087, 187649990066175
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history;
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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) = 3*a(n-1)+14*a(n-2)-48*a(n-3)+32*a(n-4) for n>5.
G.f.: (1-x-15*x^2+16*x^3+48*x^4-64*x^5) / ((1-x)*(1-2*x)*(1-4*x)*(1+4*x)).
(End)
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MATHEMATICA
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rule=141; 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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PROG
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(Python) print([1, 2] + [2**n*(4**(n//2) - 1)//3 + 2**(n-1) - 1 for n in range(2, 50)]) # Karl V. Keller, Jr., Sep 22 2021
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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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