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A115339 a(2n-1)=F(n+1), a(2n)=L(n), where F(n) and L(n) are the Fibonacci and the Lucas sequences. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 9 19:36 EST 2022. Contains 358703 sequences. (Running on oeis4.)