OFFSET
0,3
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 linear recurrences with constant coefficients, signature (-1,3,-1).
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
MATHEMATICA
CoefficientList[Series[(1/(1-x))/(1+2x-x^2), {x, 0, 50}], x] (* Harvey P. Dale, Mar 20 2011 *)
PROG
(PARI) Vec((1-x)^(-1)/(1+2*x-x^2)+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012
CROSSREFS
KEYWORD
sign,easy
AUTHOR
N. J. A. Sloane, Nov 17 2002
STATUS
approved