

A115339


a(2n1)=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
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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(n2).
G.f.: x*( 1xx^22*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 !! (n1)
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*(1xx^22*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



