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A153893
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a(n) = 3*2^n - 1.
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20
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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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A020944(a(n)) = 0. - Reinhard Zumkeller, Mar 13 2011
a(n) + a(n-1)^2 is a perfect square. - Vincenzo Librandi, Oct 28 2011
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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Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-2).
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FORMULA
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a(n) = a(n-1)*2 + 1, a(0)=2.
a(n) = A083329(n+1).
a(n) = A055010(n+1).
G.f.: (2 - x)/((1-x)(1-2x)). - R. J. Mathar, Feb 13 2009
a(n) = A083416(2n) = A033484(n) + 1. - Philippe Deléham, Apr 14 2013
From G. C. Greubel, Sep 01 2016: (Start)
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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Table[3*2^n - 1 , {n, 0, 25}] (* G. C. Greubel, Sep 01 2016 *)
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PROG
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(MAGMA) [3*2^n-1: n in [0..30]]; // Vincenzo Librandi, Oct 28 2011
(PARI) a(n)=3*2^n-1 \\ Charles R Greathouse IV, Sep 24 2015
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CROSSREFS
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Cf. A283508.
Sequence in context: A133489 A060153 A086219 * A083329 A055010 A266550
Adjacent sequences: A153890 A153891 A153892 * A153894 A153895 A153896
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KEYWORD
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nonn,easy
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AUTHOR
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Vladimir Joseph Stephan Orlovsky, Jan 03 2009
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EXTENSIONS
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Edited by N. J. A. Sloane, Feb 14 2009
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STATUS
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approved
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