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1, 1, 1, -1, 3, -5, 9, -15, 25, -41, 67, -109, 177, -287, 465, -753, 1219, -1973, 3193, -5167, 8361, -13529, 21891, -35421, 57313, -92735, 150049, -242785, 392835, -635621, 1028457, -1664079, 2692537, -4356617, 7049155, -11405773, 18454929
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,5
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COMMENTS
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Binomial transform of A128587 = A128588: (1, 2, 4, 6, 10, 16, 26, ...).
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LINKS
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FORMULA
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a(n) = -2*a(n-1) + a(n-3) = (-1)^n*(1 - A118658(n-1)).
G.f.: x*(1+3*x+3*x^2)/((1+x)*(1+x-x^2)). (End)
a(n) = (-1)^(n-1)*(2*Fibonacci(n-2) - 1). - G. C. Greubel, Jul 10 2019
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EXAMPLE
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a(5) = 3 = ( -3, 8, 0, -7, 5).
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MATHEMATICA
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Table[(-1)^(n-1)*(2*Fibonacci[n-2] -1), {n, 40}] (* G. C. Greubel, Jul 10 2019 *)
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PROG
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(PARI) vector(40, n, f=fibonacci; (-1)^(n-1)*(2*f(n-2)-1)) \\ G. C. Greubel, Jul 10 2019
(Magma) [(-1)^(n-1)*(2*Fibonacci(n-2)-1): n in [1..40]]; // G. C. Greubel, Jul 10 2019
(Sage) [(-1)^(n-1)*(2*fibonacci(n-2)-1) for n in (1..40)] # G. C. Greubel, Jul 10 2019
(GAP) List([1..40], n-> (-1)^(n-1)*(2*Fibonacci(n-2)-1)); # G. C. Greubel, Jul 10 2019
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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EXTENSIONS
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Deleted certain dangerous or potentially dangerous links. - N. J. A. Sloane, Jan 30 2021
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STATUS
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approved
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