A025169 a(n) = 2*Fibonacci(2*n+2).
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
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..200
- Hacène Belbachir, Soumeya Merwa Tebtoub, László Németh, Ellipse Chains and Associated Sequences, J. Int. Seq., Vol. 23 (2020), Article 20.8.5.
- 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).
Programs
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GAP
List([0..30], n-> 2*Fibonacci(2*n+2) ); # G. C. Greubel, Jan 16 2020
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Haskell
a025169 n = a025169_list !! n a025169_list = 2 : 6 : zipWith (-) (map (* 3) $ tail a025169_list) a025169_list -- Reinhard Zumkeller, Apr 08 2012
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Magma
[2*Fibonacci(2*n+2): n in [0..30]]; // Vincenzo Librandi, Jul 11 2011
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Magma
R
:=PowerSeriesRing(Integers(), 30); Coefficients(R!( 2/(1-3*x + x^2) )); // Marius A. Burtea, Jan 16 2020 -
Maple
seq( 2*fibonacci(2*n+2), n=0..30); # G. C. Greubel, Jan 16 2020
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Mathematica
Table[2Fibonacci[2n+2], {n,0,30}] (* or *) CoefficientList[Series[2/(1-3x+x^2), {x,0,30}], x] (* Michael De Vlieger, Mar 09 2016 *) LinearRecurrence[{3, -1}, {2, 6}, 30] (* Jean-François Alcover, Sep 27 2017 *) -
PARI
a(n)=2*fibonacci(2*n+2)
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Sage
[2*fibonacci(2*n+2) for n in (0..30)] # G. C. Greubel, Jan 16 2020
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
Extensions
Better description from Michael Somos
Comments