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A052940
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a(0) = 1; for n > 0, 3*2^n - 1.
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6
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1, 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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| A simple regular expression.
a(n) = A107909(A023548(n+1)) for n>1. - Reinhard Zumkeller, May 28 2005
Numbers n>1 such that [a(n-1)]^2+a(n) is square. Ex:5^2+11=6^2; 11^2+23=12^2. [From Vincenzo Librandi, Aug 06 2010]
Numerator of the sum of terms at the n-th level of the Calkin-Wilf tree. [From Carl Najafi, Jul 10 2011]
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LINKS
| INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 931
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FORMULA
| G.f.: -(-2*x+2*x^2-1)/(-1+2*x)/(-1+x)
a(n) = +3*a(n-1) -2*a(n-2).
Binomial transform of 3-0^n-(-1)^n=(1, 4, 2, 4, 2, 4, 2, .......). - Paul Barry, Jun 30 2003
Row sums of triangle A134060 - Gary W. Adamson, Oct 05 2007
Equals row sums of triangle A140182 - Gary W. Adamson, May 11 2008
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MAPLE
| spec := [S, {S=Prod(Sequence(Union(Z, Z)), Union(Sequence(Z), Z, Z))}, unlabeled ]: seq(combstruct[count ](spec, size=n), n=0..20);
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CROSSREFS
| Apart from initial terms, same as A055010 and A083329.
Cf. A134060.
Cf. A140182.
Sequence in context: A107010 A175942 A181669 * A191304 A102444 A132177
Adjacent sequences: A052937 A052938 A052939 * A052941 A052942 A052943
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KEYWORD
| easy,nonn
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AUTHOR
| encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu), Jun 08 2000
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