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A022112 Fibonacci sequence beginning 2, 6. 11
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

For n>=3 the number of perfect matchings in the n-antiprism graph. - Andrew Howroyd, May 17 2017

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..1000

Tanya Khovanova, Recursive Sequences

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).

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

MATHEMATICA

LinearRecurrence[{1, 1}, {2, 6}, 40] (* Harvey P. Dale, Apr 21 2012 *)

2 LucasL[Range[30]] (* Alonso del Arte, Sep 25 2013 *)

PROG

(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

CROSSREFS

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

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified September 26 15:27 EDT 2017. Contains 292531 sequences.