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Search: id:A010903
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| A010903 |
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Pisot sequence E(3,13), a(n)=[ a(n-1)^2/a(n-2)+1/2 ]. |
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+0
2
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| 3, 13, 56, 241, 1037, 4462, 19199, 82609, 355448, 1529413, 6580721, 28315366, 121834667, 524227237, 2255632184, 9705479209, 41760499493, 179686059838, 773148800711, 3326685824041, 14313982718072
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OFFSET
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0,1
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COMMENT
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According to Boyd (Acta Arithm. 32 (1977) p 89), quoting Pisot, every E(3,.) sequence satisfies a linear recurrence of at most order 3. Here this is easily derived from the first terms of the sequence. Sequence equals A010920 for at least the first 32600 terms and maybe more. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 26 2008
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REFERENCES
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D. W. Boyd, Some integer sequences related to the Pisot sequences, Acta Arithmetica, 34 (1979), 295-305.
D. W. Boyd, Linear recurrence relations for some generalized Pisot sequences, Advances in Number Theory ( Kingston ON, 1991) 333-340, Oxford Sci. Publ., Oxford Univ. Press, New York, 1993.
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FORMULA
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a(n)=5a(n-1)-3a(n-2) = 3*A116415(n)-2*A116415(n-1). O.g.f.: (3-2x)/(1-5x+3x^2). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 26 2008
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CROSSREFS
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Sequence in context: A006225 A100588 A081952 this_sequence A010920 A095934 A151220
Adjacent sequences: A010900 A010901 A010902 this_sequence A010904 A010905 A010906
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KEYWORD
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nonn
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AUTHOR
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Simon Plouffe (simon.plouffe(AT)gmail.com)
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