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A346513
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a(n) = Fibonacci(n+1)^3 - Fibonacci(n)^3.
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2
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1, 0, 7, 19, 98, 387, 1685, 7064, 30043, 127071, 538594, 2281015, 9663353, 40933296, 173398367, 734523803, 3111498370, 13180509531, 55833549037, 236514685384, 1001892323411, 4244083925895, 17978228112962, 76156996238639, 322606213292593, 1366581849044832
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OFFSET
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0,3
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COMMENTS
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The version related to sum of consecutive Fibonacci numbers cubed is given by A110224.
a(n+1) is divisible by Fibonacci(n). The related quotient sequence is provided by A061646, from its 3rd term.
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LINKS
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FORMULA
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a(n) = F(n-1)*(2*F(n+1)^2+(-1)^(n+1)), n>0.
G.f.: (x-1)*(x^2+2*x-1)/((x^2+4*x-1)*(x^2-x-1)). - Alois P. Heinz, Jul 21 2021
For n >= 2, a(n) is the numerator of the continued fraction [1,...,1, 3 ,1,...,1, 2 ,1,...,1] with three runs of 1's each of length n-2. For example, a(5)=387 which is the numerator of the continued fraction [1,1,1, 3 ,1,1,1, 2 ,1,1,1]. - Greg Dresden, Jan 01 2022
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MATHEMATICA
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Differences[Fibonacci[Range[0, 26]]^3] (* Amiram Eldar, Jul 22 2021 *)
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PROG
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(PARI) a(n) = fibonacci(n+1)^3 - fibonacci(n)^3; \\ Michel Marcus, Jul 22 2021
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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