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A141725
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a(n) = 4^(n+1) - 3.
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11
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1, 13, 61, 253, 1021, 4093, 16381, 65533, 262141, 1048573, 4194301, 16777213, 67108861, 268435453, 1073741821, 4294967293, 17179869181, 68719476733, 274877906941, 1099511627773, 4398046511101, 17592186044413, 70368744177661
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OFFSET
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0,2
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COMMENTS
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Inverse binomial transform yields A003946 with A003946(1)=4 deleted. - R. J. Mathar, Sep 13 2008
Starting with n=1, binary numbers of the form 1X01 where X is an odd number of 1's. - Brad Clardy, Mar 22 2011
Column 4 of A193871. - Omar E. Pol, Aug 22 2011
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Mattia Fregola, Elementary Cellular Automata Rule 1 generating OEIS sequence A277799, A058896, A141725, A002450
Index entries for linear recurrences with constant coefficients, signature (5, -4).
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FORMULA
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a(n) = 10*A001045(2*n) + A001045(2*n+1).
a(n) = 4*a(n-1) + 9 for n>0, a(0)=1.
a(n) = A036563(2*n+2).
G.f.: (1 + 8*x)/((1 - x)*(1 - 4*x)). - R. J. Mathar, Sep 13 2008
a(n) = 4^n - 3, with offset 1. - Omar E. Pol, Aug 22 2011
a(n) = 5*a(n-1) - 4*a(n-2) for n>1, a(0)=1, a(1)=13. - Harvey P. Dale, Sep 25 2011
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MAPLE
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a:= n-> 4^(n+1)-3: seq(a(n), n=0..25); # Muniru A Asiru, Feb 20 2018
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MATHEMATICA
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4^(Range[2, 25]-1)-3 (* or *) LinearRecurrence[{5, -4}, {1, 13}, 25] (* or *) NestList[4#+9&, 1, 25] (* Harvey P. Dale, Sep 25 2011 *)
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PROG
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(MAGMA) [4^(n+1)-3: n in [0..30]]; // Vincenzo Librandi, Aug 08 2011
(PARI) a(n)=4^(n+1)-3 \\ Charles R Greathouse IV, Oct 07 2015
(GAP) List([0..25], n -> 4^(n+1)-3); # Muniru A Asiru, Feb 20 2018
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CROSSREFS
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Cf. A001045, A036563.
Sequence in context: A252970 A047673 A231800 * A279762 A147185 A122885
Adjacent sequences: A141722 A141723 A141724 * A141726 A141727 A141728
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KEYWORD
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nonn,easy
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AUTHOR
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Paul Curtz, Sep 13 2008
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EXTENSIONS
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Edited by N. J. A. Sloane, Sep 13 2008
More terms from R. J. Mathar, Sep 13 2008
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STATUS
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approved
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