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A077921
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Expansion of (1-x)^(-1)/(1+2*x-x^2).
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3
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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
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OFFSET
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0,3
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COMMENTS
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Partial sums of sequence of signed Pell numbers (-1)^n*A000129(n). - Paul Barry, May 09 2003
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LINKS
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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).
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FORMULA
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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
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MATHEMATICA
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CoefficientList[Series[(1/(1-x))/(1+2x-x^2), {x, 0, 50}], x] (* Harvey P. Dale, Mar 20 2011 *)
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PROG
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(PARI) Vec((1-x)^(-1)/(1+2*x-x^2)+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012
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CROSSREFS
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-a(-3-n) = A048739(n).
Sequence in context: A244583 A261031 * A097076 A003608 A248423 A319565
Adjacent sequences: A077918 A077919 A077920 * A077922 A077923 A077924
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KEYWORD
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sign,easy
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AUTHOR
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N. J. A. Sloane, Nov 17 2002
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STATUS
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approved
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