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A141725
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a(n) = 4^(n+1)-3 .
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5
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Inverse binomial transform yields A003946 with A003946(1)=4 deleted. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 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
| Vincenzo Librandi, Table of n, a(n) for n = 0..1000
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FORMULA
| a(n) = 10*A001045(2n) + A001045(2n+1).
a(n)=4a(n-1)+9, a(0)=1. a(n)=A036563(2n+2).
G.f.: (1+8x)/((1-x)(1-4x)). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 13 2008]
a(n) = 4^n-3, with offset 1. - Omar E. Pol, Aug 22 2011
a(0)=1, a(1)=13, a(n)=5*a(n-1)-4*a(n-2) [From Harvey P. Dale, Sep 25 2011]
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MATHEMATICA
| 4^(Range[2, 25]-1)-3 (* or *) LinearRecurrence[{5, -4}, {1, 13}, 25] (* or *) NestList[4#+9&, 1, 25] (* From Harvey P. Dale, Sep 25 2011 *)
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PROG
| (MAGMA) [4^(n+1)-3: n in [0..30]]; // Vincenzo Librandi, Aug 08 2011
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CROSSREFS
| Sequence in context: A139880 A127876 A047673 * A147185 A122885 A135535
Adjacent sequences: A141722 A141723 A141724 * A141726 A141727 A141728
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KEYWORD
| nonn,easy
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AUTHOR
| Paul Curtz (bpcrtz(AT)free.fr), Sep 13 2008
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EXTENSIONS
| Edited by N. J. A. Sloane (njas(AT)research.att.com), Sep 13 2008
More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 13 2008
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