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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
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refs;
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history;
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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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G. C. Greubel, Table of n, a(n) for n = 1..1000
Yüksel Soykan, Summing Formulas For Generalized Tribonacci Numbers, arXiv:1910.03490 [math.GM], 2019.
Index entries for linear recurrences with constant coefficients, signature (-2,0,1).
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FORMULA
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Row sums of triangle A128586, inverse binomial transform of A128588.
From R. J. Mathar, Jun 03 2009: (Start)
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+3) = (-1)^n * A001595(n) for all n>=0. - M. F. Hasler and Franklin T. Adams-Watters, Sep 30 2009
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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Cf. A128586, A128588.
This is a signed version of A001595. [Franklin T. Adams-Watters, Sep 30 2009]
Cf. A000045.
Sequence in context: A053523 A053522 A053521 * A001595 A092369 A298340
Adjacent sequences: A128584 A128585 A128586 * A128588 A128589 A128590
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KEYWORD
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sign
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AUTHOR
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Gary W. Adamson, Mar 11 2007
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EXTENSIONS
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More terms from R. J. Mathar, Jun 03 2009
Duplicate of a formula removed by R. J. Mathar, Oct 23 2009
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STATUS
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approved
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