A022112 Fibonacci sequence beginning 2, 6.
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
Offset: 0
Links
- 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).
Crossrefs
Cf. sequences with formula Fibonacci(n+k)+Fibonacci(n-k) listed in A280154.
Programs
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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
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Mathematica
LinearRecurrence[{1, 1}, {2, 6}, 40] (* Harvey P. Dale, Apr 21 2012 *) 2 LucasL[Range[30]] (* Alonso del Arte, Sep 25 2013 *) -
PARI
a(n)=4*fibonacci(n+2)-2*fibonacci(n+1) \\ Charles R Greathouse IV, Oct 07 2015
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PARI
Vec(2*(1 + 2*x) / (1 - x - x^2) + O(x^60)) \\ Colin Barker, Oct 27 2017
Formula
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)
Comments