A077921 Expansion of (1-x)^(-1)/(1+2*x-x^2).

1, -1, 4, -8, 21, -49, 120, -288, 697, -1681, 4060, -9800, 23661, -57121, 137904, -332928, 803761, -1940449, 4684660, -11309768, 27304197, -65918161, 159140520, -384199200, 927538921, -2239277041, 5406093004, -13051463048, 31509019101, -76069501249, 183648021600

Offset: 0

Author

N. J. A. Sloane, Nov 17 2002

Keywords

• sign
• easy

Comments

Partial sums of sequence of signed Pell numbers (-1)^n*A000129(n). - Paul Barry, May 09 2003

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for two-way infinite sequences
• Index entries for linear recurrences with constant coefficients, signature (-1,3,-1).

Crossrefs

-a(-3-n) = A048739(n).

Programs

Mathematica

CoefficientList[Series[(1/(1-x))/(1+2x-x^2), {x,0,50}], x] (* Harvey P. Dale, Mar 20 2011 *)

PARI

Vec((1-x)^(-1)/(1+2*x-x^2)+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012

Formula

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

From Colin Barker, Apr 15 2016: (Start)

a(n) = -a(n-1)+3*a(n-2)-a(n-3) for n>2.

a(n) = (2-(-1-sqrt(2))^(1+n)-(-1+sqrt(2))^(1+n))/4.

(End)

E.g.f.: (1/4)*(2*exp(x) + (1 + sqrt(2))*exp((-1-sqrt(2))*x) - (sqrt(2) - 1)*exp((sqrt(2)-1)*x)). - Ilya Gutkovskiy, Apr 15 2016