A128587 Row sums of A128586.

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

Offset: 1

Author

Gary W. Adamson, Mar 11 2007

Keywords

• sign

Comments

Binomial transform of A128587 = A128588: (1, 2, 4, 6, 10, 16, 26, ...).

Examples

			a(5) = 3 = ( -3, 8, 0, -7, 5).
		

Links

• 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).

Crossrefs

Cf. A128586, A128588.

This is a signed version of A001595. - Franklin T. Adams-Watters, Sep 30 2009

Cf. A000045.

Programs

GAP

List([1..40], n-> (-1)^(n-1)*(2*Fibonacci(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

Mathematica

Table[(-1)^(n-1)*(2*Fibonacci[n-2] -1), {n, 40}] (* G. C. Greubel, Jul 10 2019 *)

PARI

vector(40, n, f=fibonacci; (-1)^(n-1)*(2*f(n-2)-1)) \\ 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

Formula

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

Extensions

More terms from R. J. Mathar, Jun 03 2009

Duplicate of a formula removed by R. J. Mathar, Oct 23 2009

Deleted certain dangerous or potentially dangerous links. - N. J. A. Sloane, Jan 30 2021