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A153893
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a(n) = 3*2^n - 1.
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26
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2, 5, 11, 23, 47, 95, 191, 383, 767, 1535, 3071, 6143, 12287, 24575, 49151, 98303, 196607, 393215, 786431, 1572863, 3145727, 6291455, 12582911, 25165823, 50331647, 100663295, 201326591, 402653183, 805306367, 1610612735, 3221225471
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OFFSET
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0,1
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COMMENTS
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Number of distinct continued fractions of n terms chosen from {1,2}. - Clark Kimberling, Jul 20 2015
Also, the decimal representation of the x-axis, from the origin to the right edge, of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 643", based on the 5-celled von Neumann neighborhood, initialized with a single black (ON) cell at stage zero. See A283508. - Robert Price, Mar 09 2017
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LINKS
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FORMULA
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a(n) = a(n-1)*2 + 1, a(0)=2.
a(n) = 3*a(n-1) - 2*a(n-2).
E.g.f.: 3*exp(2*x) - exp(x). (End)
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MATHEMATICA
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LinearRecurrence[{3, -2}, {2, 5}, 40] (* Harvey P. Dale, Mar 01 2024 *)
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PROG
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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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EXTENSIONS
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STATUS
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approved
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