A087171 Expansion of (1 + 5*x)/(1 + 9*x + 25*x^2).

1, -4, 11, 1, -284, 2531, -15679, 77836, -308549, 831041, 234356, -22885229, 200108161, -1228842724, 6056880491, -23790856319, 62695694596, 30510156611, -1841983774399, 15815100054316, -96286306128869, 471199253801921, -1833635630995564, 4722739333912051

Offset

0,2

Comments

For positive n, a(n) equals the 5^n times the permanent of the (2n) X (2n) tridiagonal matrix with 1/sqrt(5)'s along the main diagonal, and i's along the superdiagonal and the subdiagonal (where i is the imaginary unit). - John M. Campbell, Jul 08 2011

Links

Table of n, a(n) for n=0..23.

Index entries for linear recurrences with constant coefficients, signature (-9,-25).

Formula

G.f.: (1 + 5*x)/(1 + 9*x + 25*x^2).

a(n) = -9*a(n-1) - 25*a(n-2), a(0)=1, a(1)=-4.

a(n) = Sum_{k=0..n} binomial(n+k,2*k)*(-5)^(n-k).

Mathematica

CoefficientList[Series[(1 + 5x)/(25x^2 + 9x + 1), {x, 0, 25}], x]
LinearRecurrence[{-9, -25}, {1, -4}, 30] (* Harvey P. Dale, Sep 10 2017 *)

Crossrefs

Sequence in context: A091389 A175668 A113249 * A282026 A066333 A230870

Adjacent sequences: A087168 A087169 A087170 * A087172 A087173 A087174

Keyword

easy,sign

Author

Mario Catalani (mario.catalani(AT)unito.it), Aug 22 2003

Status

approved