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A022112
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Fibonacci sequence beginning 2, 6.
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17
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2, 6, 8, 14, 22, 36, 58, 94, 152, 246, 398, 644, 1042, 1686, 2728, 4414, 7142, 11556, 18698, 30254, 48952, 79206, 128158, 207364, 335522, 542886, 878408, 1421294, 2299702, 3720996, 6020698, 9741694, 15762392, 25504086, 41266478, 66770564, 108037042
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OFFSET
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0,1
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COMMENTS
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For n>=3 the number of perfect matchings in the n-antiprism graph. - Andrew Howroyd, May 17 2017
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LINKS
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Eric Weisstein's World of Mathematics, Matching
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FORMULA
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a(n) = 4*Fibonacci(n+2) - 2*Fibonacci(n+1). - Gary Detlefs, Dec 21 2010
G.f.: ( -2-4*x ) / ( -1+x+x^2 ). - R. J. Mathar, Mar 11 2011
a(n) = Fibonacci(n-2) + Fibonacci(n+4). - Gary Detlefs, Mar 31 2012
a(n) = L(n - 1) + L(n) + L(n + 1), for n > 0, where L(n) is the n-th Lucas number (A000204). - Alonso del Arte, Sep 25 2013
a(n) = (2^(-n)*((1-sqrt(5))^n*(-5+sqrt(5)) + (1+sqrt(5))^n*(5+sqrt(5)))) / sqrt(5).
a(n) = a(n-1) + a(n-2) for > 1.
(End)
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MATHEMATICA
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LinearRecurrence[{1, 1}, {2, 6}, 40] (* Harvey P. Dale, Apr 21 2012 *)
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PROG
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(Haskell)
a022112 n = a022112_list !! n
a022112_list = 2 : 6 : zipWith (+) (tail a022112_list) a022112_list
(PARI) Vec(2*(1 + 2*x) / (1 - x - x^2) + O(x^60)) \\ Colin Barker, Oct 27 2017
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CROSSREFS
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Cf. sequences with formula Fibonacci(n+k)+Fibonacci(n-k) listed in A280154.
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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