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Search: id:A003482
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| A003482 |
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a(n) = 7a(n-1) - a(n-2) + 4.
(Formerly M3988)
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+0
2
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| 0, 5, 39, 272, 1869, 12815, 87840, 602069, 4126647, 28284464, 193864605, 1328767775, 9107509824, 62423800997, 427859097159, 2932589879120
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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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
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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. M. Tanny and M. Zuker, On a unimodal sequence of binomial coefficients, Discrete Math. 9 (1974), 79-89.
H. Harborth, Fermat-like binomial equations, Applications of Fibonacci numbers, Proc. 2nd Int. Conf., San Jose/Ca., August 1986, 1-5 (1988).
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LINKS
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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.
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FORMULA
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a(n)=fibonacci(2*n)*fibonacci(2*n+3).
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MAPLE
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A003482:=z*(-5+z)/(z-1)/(z**2-7*z+1); [Conjectured by S. Plouffe in his 1992 dissertation.]
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CROSSREFS
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Cf. A001109.
Equals A033888 - 1.
Sequence in context: A123614 A075135 A053573 this_sequence A135849 A105426 A115187
Adjacent sequences: A003479 A003480 A003481 this_sequence A003483 A003484 A003485
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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