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A007502
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Les Marvin sequence: a(n) = F(n)+(n-1)*F(n-1), F() = Fibonacci numbers.
(Formerly M1170)
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9
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1, 2, 4, 9, 17, 33, 61, 112, 202, 361, 639, 1123, 1961, 3406, 5888, 10137, 17389, 29733, 50693, 86204, 146246, 247577, 418299, 705479, 1187857, 1997018, 3352636, 5621097, 9412937, 15744681, 26307469, 43912648
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OFFSET
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1,2
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COMMENTS
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Denominators of convergents of the continued fraction with the n partial quotients: [1;1,1,...(n-1 1's)...,1,n], starting with [1], [1;2], [1;1,3], [1;1,1,4], ... Numerators are A088209(n-1). - Paul D. Hanna, Sep 23 2003
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REFERENCES
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Les Marvin, Problem, J. Rec. Math., Vol. 10 (No. 3, 1976-1977), p. 213.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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a(n) = 2*a(n-1) + a(n-2) - 2*a(n-3) - a(n-4) for n>3, a(0)=1, a(1)=2, a(2)=4, a(3)=9. - Harvey P. Dale, Jul 13 2011
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EXAMPLE
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a(7) = F(7)+6*F(6) = 13+6*8 = 61.
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MATHEMATICA
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Table[Fibonacci[n]+(n-1)*Fibonacci[n-1], {n, 40}] (* or *) LinearRecurrence[ {2, 1, -2, -1}, {1, 2, 4, 9}, 40](* Harvey P. Dale, Jul 13 2011 *)
f[n_] := Denominator@ FromContinuedFraction@ Join[ Table[1, {n}], {n + 1}]; Array[f, 30, 0] (* Robert G. Wilson v, Mar 04 2012 *)
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PROG
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(Haskell)
a007502 n = a007502_list !! (n-1)
a007502_list = zipWith (+) a045925_list $ tail a000045_list
(Julia) # The function 'fibrec' is defined in A354044.
n == 0 && return BigInt(1)
a, b = fibrec(n-1)
(n-1)*a + b
end
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CROSSREFS
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KEYWORD
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nonn,nice,easy
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AUTHOR
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STATUS
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approved
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