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A127984
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Numbers of the form (n/3 + 7/9)*2^(n - 1) + (-1)^n/9.
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3
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1, 3, 7, 17, 39, 89, 199, 441, 967, 2105, 4551, 9785, 20935, 44601, 94663, 200249, 422343, 888377, 1864135, 3903033, 8155591, 17010233, 35418567, 73633337, 152859079, 316902969, 656175559, 1357090361, 2803659207, 5786275385
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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REFERENCES
| Bosma, W., 2001. Signed bits and fast exponentiation. J. Th. des Nombres de Bordeaux Vol.13, Fasc. 1
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LINKS
| Bosma, W., Signed bits and fast exponentiation.
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FORMULA
| a(n) = (n/3 + 7/9)*2^(n - 1) + (-1)^n/9
O.g.f.: -x*(-1+2x^2)/[(-1+2x)^2*(1+x)]. a(n)=3*a(n-1)-4*a(n-3). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 04 2008
a(n)+a(n+1)=A087447(n+1). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 21 2009]
A172481(n) = A127984(n) + 2^(n-1). Application: Problem 11623, AMM 119 (2012) 161. [Stephen J. Herschkorn, 11 Feb 2012]
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MATHEMATICA
| Table[(n/3 + 7/9)2^(n - 1) + (-1)^n/9, {n, 1, 50}] (*Artur Jasinski*)
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CROSSREFS
| Cf. A073371, A127976, A127978, A127979, A127980, A127981, A127982, A127983, A073371, A000337, A172481.
Sequence in context: A141199 A003478 A119587 * A157029 A191825 A077927
Adjacent sequences: A127981 A127982 A127983 * A127985 A127986 A127987
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KEYWORD
| nonn,changed
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AUTHOR
| Artur Jasinski (grafix(AT)csl.pl), Feb 09 2007
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