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A087123
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a(n) = Fibonacci(n+1) - (-1)^n*Fibonacci(n).
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3
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1, 2, 1, 5, 2, 13, 5, 34, 13, 89, 34, 233, 89, 610, 233, 1597, 610, 4181, 1597, 10946, 4181, 28657, 10946, 75025, 28657, 196418, 75025, 514229, 196418, 1346269, 514229, 3524578, 1346269, 9227465, 3524578, 24157817, 9227465, 63245986, 24157817
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OFFSET
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0,2
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COMMENTS
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Binomial transform is Fibonacci(n) + Fibonacci(2n+1) = A087124(n).
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LINKS
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FORMULA
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a(2n) = Fibonacci(2n-1), a(2n+1) = Fibonacci(2n+3).
G.f.: (1-x)*(1+3*x+x^2)/((1+x-x^2)*(1-x-x^2)). - Colin Barker, Apr 16 2012
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MAPLE
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MATHEMATICA
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MapIndexed[#2 - (-1)^#1*#3 & @@ {First@ #2 - 1, Last@ #1, First@ #1} &, Partition[Fibonacci@ Range[0, 36], 2, 1]] (* or *)
CoefficientList[Series[(1 - x) (1 + 3 x + x^2)/((1 + x - x^2) (1 - x - x^2)), {x, 0, 38}], x] (* Michael De Vlieger, Oct 06 2017 *)
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PROG
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(PARI) a(n) = fibonacci(n+1)-(-1)^n*fibonacci(n); \\ Altug Alkan, Oct 06 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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STATUS
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approved
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