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A003482
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a(n) = 7a(n-1) - a(n-2) + 4.
(Formerly M3988)
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2
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0, 5, 39, 272, 1869, 12815, 87840, 602069, 4126647, 28284464, 193864605, 1328767775, 9107509824, 62423800997, 427859097159, 2932589879120, 20100270056685, 137769300517679, 944284833567072, 6472224534451829, 44361286907595735, 304056783818718320
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| The values (a(n),x(n)), n >= 2, x(n)=fibonacci(2*n+2)*fibonacci(2*n+3), are the integer solutions (a,x) of the equation binomial(x+1,a+1) + binomial(x+2,a+1)= binomial(x+3,a+1) - Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de)
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REFERENCES
| H. Harborth, Fermat-like binomial equations, Applications of Fibonacci numbers, Proc. 2nd Int. Conf., San Jose/Ca., August 1986, 1-5 (1988).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
S. M. Tanny and M. Zuker, On a unimodal sequence of binomial coefficients, Discrete Math. 9 (1974), 79-89.
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..1000
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 (8,-8,1).
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FORMULA
| a(n) = fibonacci(2*n) * fibonacci(2*n+3).
a(n) = fibonacci(2*n+2)^2 - fibonacci(2*n+1)^2. [From Gary Detlefs, Oct 12 2011]
a(n) = A033888(n) - 1.
a(n) = 8*a(n-1) -8*a(n-2) +a(n-3). - Orlovsky - Librandi, Jan 22 2012
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MAPLE
| A003482:=z*(-5+z)/(z-1)/(z**2-7*z+1); [Conjectured by S. Plouffe in his 1992 dissertation.]
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MATHEMATICA
| LinearRecurrence[{8, -8, 1}, {0, 5, 39}, 30] (* From Vladimir Joseph Stephan Orlovsky, Jan 21 2012 *)
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CROSSREFS
| Cf. A001109.
Sequence in context: A075135 A202391 A053573 * A201442 A135849 A105426
Adjacent sequences: A003479 A003480 A003481 * A003483 A003484 A003485
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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