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A115339
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a(2n-1)=F(n+1), a(2n)=L(n), where F(n) and L(n) are the Fibonacci and the Lucas sequences.
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4
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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
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1,3
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COMMENTS
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Alternate Fibonacci and Lucas sequence respecting their natural order.
See A116470 for an essentially identical sequence.
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LINKS
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FORMULA
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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
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MATHEMATICA
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f[n_] := If[OddQ@n, Fibonacci[(n + 3)/2], Fibonacci[n/2 - 1] + Fibonacci[n/2 + 1]]; Array[f, 50] (* Robert G. Wilson v *)
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PROG
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(Haskell)
a115339 n = a115339_list !! (n-1)
a115339_list = [1, 1, 2, 3] ++
zipWith (+) a115339_list (drop 2 a115339_list)
(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
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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