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A022112
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Fibonacci sequence beginning 2, 6.
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14
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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
(list;
graph;
refs;
listen;
history;
text;
internal format)
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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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Reinhard Zumkeller, Table of n, a(n) for n = 0..1000
Tanya Khovanova, Recursive Sequences
Yun-Tak Oh, Hosho Katsura, Hyun-Yong Lee and Jung Hoon Han, Proposal of a spin-one chain model with competing dimer and trimer interactions, arXiv:1709.01344 [cond-mat.str-el], 2017.
Eric Weisstein's World of Mathematics, Antiprism Graph
Eric Weisstein's World of Mathematics, Independent Edge Set
Eric Weisstein's World of Mathematics, Matching
Eric Weisstein's World of Mathematics, Perfect Matching
Eric Weisstein's World of Mathematics, Maximum Independent Edge Set
Index entries for linear recurrences with constant coefficients, signature (1,1).
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FORMULA
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a(n) = 4*Fibonacci(n+2) - 2*Fibonacci(n+1). - Gary Detlefs, Dec 21 2010
a(n) = 2*A000204(n+1). - R. J. Mathar, Mar 11 2011
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) = L(n + 3) - L(n). - Bruno Berselli, Jun 15 2017
From Colin Barker, Oct 27 2017: (Start)
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 *)
2 LucasL[Range[30]] (* Alonso del Arte, Sep 25 2013 *)
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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
-- Reinhard Zumkeller, Apr 08 2012
(PARI) a(n)=4*fibonacci(n+2)-2*fibonacci(n+1) \\ Charles R Greathouse IV, Oct 07 2015
(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.
Sequence in context: A117588 A174229 A187217 * A107019 A269831 A048133
Adjacent sequences: A022109 A022110 A022111 * A022113 A022114 A022115
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane
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STATUS
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approved
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