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A005592
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F(2n+1)+F(2n-1)-1.
(Formerly M1619)
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4
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2, 6, 17, 46, 122, 321, 842, 2206, 5777, 15126, 39602, 103681, 271442, 710646, 1860497, 4870846, 12752042, 33385281, 87403802, 228826126, 599074577, 1568397606, 4106118242, 10749957121, 28143753122, 73681302246, 192900153617
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| For any m, the maximum element in the continued fraction of F(2n+m)/F(m) is a(n) - Benoit Cloitre (benoit7848c(AT)orange.fr), Jan 10 2006
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REFERENCES
| M. D. McIlroy, The number of states of a dynamic storage system, Computer J., 25 (No. 3, 1982), 388-392.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..200
S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
Index to sequences with linear recurrences with constant coefficients, signature (4,-4,1).
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FORMULA
| a(n) = Lucas(2*n)-1, with Lucas(n)=A000032(n).
a(n)=floor(r^(2*n)), where r = golden ratio = (1+sqrt(5))/2.
a(n)=floor(Fibonacci(5*n)/Fibonacci(3*n)). [From Gary Detlefs (gdetlefs(AT)aol.com), Mar 11 2011]
a(n)=+4*a(n-1)-4*a(n-2)+1*a(n-3) [Joerg Arndt, Mar 11 2011].
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MAPLE
| A005592:=-(2-2*z+z**2)/(z-1)/(z**2-3*z+1); [Conjectured by S. Plouffe in his 1992 dissertation.]
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MATHEMATICA
| Table[Fibonacci[2n+1]+Fibonacci[2n-1]-1, {n, 30}] (* From Harvey P. Dale, Aug 22 2011 *)
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PROG
| sage: [lucas_number2(n, 3, 1)-1 for n in xrange(1, 29)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 06 2008
(MAGMA) [Fibonacci(2*n+1)+Fibonacci(2*n-1)-1: n in [1..30]]; // Vincenzo Librandi, Aug 23 2011
(PARI) a(n)=fibonacci(2*n+1)+fibonacci(2*n-1)-1 \\ Charles R Greathouse IV, Aug 23 2011
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CROSSREFS
| Equals A004146+1 and A005248+1. Bisection of A014217; the other bisection is A002878, which also bisects A000032.
Cf. A065034.
Sequence in context: A065068 A109961 A190050 * A102403 A200379 A032638
Adjacent sequences: A005589 A005590 A005591 * A005593 A005594 A005595
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Formulae and comments by Clark Kimberling (ck6(AT)evansville.edu), Nov 24 2010
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