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 A077921 Expansion of (1-x)^(-1)/(1+2*x-x^2). 3
 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 (list; graph; refs; listen; history; text; internal format)
 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 -a(-3-n) = A048739(n). Sequence in context: A180608 A244583 A261031 * A097076 A003608 A248423 Adjacent sequences:  A077918 A077919 A077920 * A077922 A077923 A077924 KEYWORD sign,easy AUTHOR N. J. A. Sloane, Nov 17 2002 STATUS approved

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Last modified December 16 09:06 EST 2019. Contains 330020 sequences. (Running on oeis4.)