A115339 a(2n-1)=F(n+1), a(2n)=L(n), where F(n) and L(n) are the Fibonacci and the Lucas sequences.

1, 1, 2, 3, 3, 4, 5, 7, 8, 11, 13, 18, 21, 29, 34, 47, 55, 76, 89, 123, 144, 199, 233, 322, 377, 521, 610, 843, 987, 1364, 1597, 2207, 2584, 3571, 4181, 5778, 6765, 9349, 10946, 15127, 17711, 24476, 28657, 39603, 46368, 64079, 75025, 103682, 121393, 167761

Offset

1,3

Comments

Alternate Fibonacci and Lucas sequence respecting their natural order.

See A116470 for an essentially identical sequence.

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Fibonacci Number

Eric Weisstein's World of Mathematics, Lucas Number.

Index entries for linear recurrences with constant coefficients, signature (0,1,0,1).

Formula

a(n+2) = a(n) + a(n-2).

G.f.: x*( -1-x-x^2-2*x^3 ) / ( -1+x^2+x^4 ). - R. J. Mathar, Mar 08 2011

Mathematica

f[n_] := If[OddQ@n, Fibonacci[(n + 3)/2], Fibonacci[n/2 - 1] + Fibonacci[n/2 + 1]]; Array[f, 50] (* Robert G. Wilson v *)

Prog

(Haskell)
a115339 n = a115339_list !! (n-1)
a115339_list = [1, 1, 2, 3] ++
               zipWith (+) a115339_list (drop 2 a115339_list)
-- Reinhard Zumkeller, Aug 03 2013
(PARI) x='x+O('x^50); Vec(x*(-1-x-x^2-2*x^3)/(-1+x^2+x^4)) \\ G. C. Greubel, Apr 27 2017

Crossrefs

Cf. A000045, A000032.

Cf. A000930.

Sequence in context: A343941 A280127 A237977 * A305631 A036019 A018120

Adjacent sequences: A115336 A115337 A115338 * A115340 A115341 A115342

Keyword

easy,nonn

Author

Giuseppe Coppoletta, Mar 06 2006

Extensions

More terms from Robert G. Wilson v, Apr 29 2006

Status

approved