A291535 Expansion of the series reversion of x*(1 + 2*x)/(1 - x - x^2).

1, -3, 14, -82, 541, -3833, 28479, -218927, 1726651, -13893013, 113594944, -941109972, 7883133111, -66651214993, 568062130934, -4875322862342, 42097583306171, -365467693020273, 3188024056471074, -27929166139563662, 245625484632281831, -2167751159576883103, 19192382951736683739

Offset

1,2

Comments

Reversion of g.f. for the Lucas numbers (beginning with 1) (A000204).

Links

Vaclav Kotesovec, Table of n, a(n) for n = 1..500

N. J. A. Sloane, Transforms

Eric Weisstein's World of Mathematics, Series Reversion

Index entries for reversions of series

Formula

G.f. A(x) satisfies: A(x)*(1 + 2*A(x))/(1 - A(x) - A(x)^2) = x.

a(n) ~ -(-1)^n * 5^((n+1)/2) * phi^(3*n - 9/2) / (2*sqrt(Pi)*n^(3/2)), where phi = A001622 = (1+sqrt(5))/2 is the golden ratio. - Vaclav Kotesovec, Nov 11 2017

D-finite with recurrence 2*n*a(n) +3*(7*n-10)*a(n-1) +5*(4*n-9)*a(n-2) +5*(n-3)*a(n-3)=0. - R. J. Mathar, Mar 24 2023

Mathematica

Rest[CoefficientList[InverseSeries[Series[x (1 + 2 x)/(1 - x - x^2), {x, 0, 23}], x], x]]

Crossrefs

Cf. A000204, A007440.

Sequence in context: A032332 A032080 A367078 * A333956 A194091 A186737

Adjacent sequences: A291532 A291533 A291534 * A291536 A291537 A291538

Keyword

sign

Author

Ilya Gutkovskiy, Aug 25 2017

Status

approved