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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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1
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| 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
For n>=1, a(n-1) is the number of generalized compositions of n when there are i+2 different types of i, (i=1,2,...). [From Milan R. Janjic (agnus(AT)blic.net), Sep 24 2010]
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REFERENCES
| 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
| 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
| Sequence in context: A100588 A081952 * A010920 A095934 A151220 A151221
Adjacent sequences: A010900 A010901 A010902 * A010904 A010905 A010906
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KEYWORD
| nonn
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AUTHOR
| Simon Plouffe (simon.plouffe(AT)gmail.com)
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