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Search: id:A018910
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| 4, 5, 7, 10, 15, 23, 36, 57, 91, 146, 235, 379, 612, 989, 1599, 2586, 4183, 6767, 10948, 17713, 28659, 46370, 75027, 121395, 196420, 317813, 514231, 832042, 1346271, 2178311, 3524580, 5702889, 9227467, 14930354, 24157819, 39088171, 63245988, 102334157, 165580143
(list; graph; listen)
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OFFSET
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0,1
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REFERENCES
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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) = Fib(n+3)+2; a(n) = 2a(n-1) - a(n-3).
G.f.: -(-4+3*x+3*x^2)/(x-1)/(x^2+x-1) = -2/(x-1)+(-x-2)/(x^2+x-1) . - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 23 2007
a(n)=2+[1/2+(1/2)*sqrt(5)]^n+(2/5)*[1/2+(1/2)*sqrt(5)]^n*sqrt(5)-(2/5)*sqrt(5)*[1/2-(1/2) *sqrt(5)]^n+[1/2-(1/2)*sqrt(5)]^n, with n>=0 - Paolo P. Lava (ppl(AT)spl.at), Jun 10 2008
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CROSSREFS
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See A008776 for definitions of Pisot sequences.
Sequence in context: A013947 A093517 A145018 this_sequence A022936 A057496 A057708
Adjacent sequences: A018907 A018908 A018909 this_sequence A018911 A018912 A018913
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KEYWORD
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nonn
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AUTHOR
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R. K. Guy (rkg(AT)cpsc.ucalgary.ca)
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