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A025169 a(n) = 2*F(2*n+2), where F(n)=A000045(n) (the Fibonacci sequence). 13
2, 6, 16, 42, 110, 288, 754, 1974, 5168, 13530, 35422, 92736, 242786, 635622, 1664080, 4356618, 11405774, 29860704, 78176338, 204668310, 535828592, 1402817466, 3672623806, 9615053952, 25172538050, 65902560198, 172535142544 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

The pairs (x, y) = (a(n), a(n+1)) satisfy  x^2 + y^2 = 3*x*y + 4. - Michel Lagneau, Feb 01 2014

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Mark W. Coffey, James L. Hindmarsh, Matthew C. Lettington, John Pryce, On Higher Dimensional Interlacing Fibonacci Sequences, Continued Fractions and Chebyshev Polynomials, arXiv:1502.03085 [math.NT], 2015 (see p. 32).

Tanya Khovanova, Recursive Sequences

Index entries for linear recurrences with constant coefficients, signature (3,-1).

FORMULA

G.f.: 2/(1 - 3*x + x^2).

a(n) = 3*a(n-1) - a(n-2).

a(n) = 2*A001906(n+1).

a(n) = A111282(n+2). - Reinhard Zumkeller, Apr 08 2012

a(n) = Fibonacci(2*n+1) + Lucas(2*n+1). - Bruno Berselli, Oct 13 2017

MATHEMATICA

Table[2 Fibonacci[2 n + 2], {n, 0, 26}] (* or *)

CoefficientList[Series[2/(1 - 3 x + x^2), {x, 0, 26}], x] (* Michael De Vlieger, Mar 09 2016 *)

LinearRecurrence[{3, -1}, {2, 6}, 27] (* Jean-Fran├žois Alcover, Sep 27 2017 *)

PROG

(PARI) a(n)=2*fibonacci(2*n+2)

(MAGMA) [2*Fibonacci(2*n+2): n in [0..30]]; // Vincenzo Librandi, Jul 11 2011

(Haskell)

a025169 n = a025169_list !! n

a025169_list = 2 : 6 : zipWith (-) (map (* 3) $ tail a025169_list) a025169_list

-- Reinhard Zumkeller, Apr 08 2012

CROSSREFS

Cf. A000032, A000045, A001906, A002878, A122367.

Sequence in context: A217194 A156664 * A111282 A115730 A191694 A224232

Adjacent sequences:  A025166 A025167 A025168 * A025170 A025171 A025172

KEYWORD

nonn,easy

AUTHOR

Wouter Meeussen

EXTENSIONS

Better description from Michael Somos

STATUS

approved

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Last modified November 19 07:02 EST 2017. Contains 294915 sequences.