A141342 A transform of the Fibonacci numbers.

1, 1, -1, 3, -13, 65, -353, 2025, -12077, 74143, -465481, 2974863, -19289821, 126594191, -839273105, 5612483619, -37814455781, 256447068841, -1749182184793, 11991887667273, -82588248514885, 571118483653841

Offset

0,4

Comments

A transform of F(n+1) by the inverse of the Riordan array (1, x*(1+x)/(1-2*x)).

Equivalently, row sums of the inverse of the Riordan array (1, x/(2-sqrt(1+4*x)).

Hankel transform is alternating sign version of A083667.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Formula

G.f.: 1/(1-2*x-2*x^2+x*sqrt(1+8*x+4*x^2)).

Conjecture: (n-1)*a(n) +4*(n-4)*a(n-1) + (65-29*n)*a(n-2) +12*(7-2*n)*a(n-3)+ 4*(4-n)*a(n-4) =0. - R. J. Mathar, Nov 14 2011

a(n) ~ (-1)^n * (5*sqrt(3)-14) * sqrt(2*sqrt(3)-3) * 2^(n+1/2) * (2+sqrt(3))^n / (121 * sqrt(Pi) * n^(3/2)). - Vaclav Kotesovec, Feb 01 2014

Mathematica

CoefficientList[Series[1/(1-2*x-2*x^2+x*Sqrt[1+8*x+4*x^2]), {x, 0, 20}], x] (* Vaclav Kotesovec, Feb 01 2014 *)

Prog

(PARI) x='x+O('x^50); Vec(1/(1-2*x-2*x^2+x*sqrt(1+8*x+4*x^2))) \\ G. C. Greubel, Mar 21 2017

Crossrefs

Cf. A141343.

Sequence in context: A284715 A364473 A186577 * A232222 A241598 A155867

Adjacent sequences: A141339 A141340 A141341 * A141343 A141344 A141345

Keyword

easy,sign

Author

Paul Barry, Jun 26 2008

Status

approved