A077989 Expansion of 1/(1+2*x+x^2-2*x^3).

1, -2, 3, -2, -3, 14, -29, 38, -19, -58, 211, -402, 477, -130, -1021, 3126, -5491, 5814, 115, -17026, 45565, -73874, 68131, 28742, -273363, 654246, -977645, 754318, 777501, -4264610, 9260355, -12701098, 7612621, 15996566, -65007949, 129244574, -161488067, 63715662, 292545891

Offset: 0

Author

N. J. A. Sloane, Nov 17 2002

Keywords

• sign
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (-2,-1,2).

Crossrefs

Cf. A077942.

Programs

GAP

a:=[1,-2,3];; for n in [4..40] do a[n]:=-2*a[n-1]-a[n-2]+2*a[n-3]; od; a; # G. C. Greubel, Jun 26 2019

Magma

R:=PowerSeriesRing(Integers(), 40); Coefficients(R!( 1/(1+2*x+x^2-2*x^3) )); // G. C. Greubel, Jun 26 2019

Mathematica

LinearRecurrence[{-2,-1,2}, {1,-2,3}, 40] (* or *) CoefficientList[Series[1/(1+2*x+x^2-2*x^3), {x,0,40}], x] (* G. C. Greubel, Jun 26 2019 *)

PARI

my(x='x+O('x^40)); Vec(1/(1+2*x+x^2-2*x^3)) \\ G. C. Greubel, Jun 26 2019

Sage

(1/(1+2*x+x^2-2*x^3)).series(x, 40).coefficients(x, sparse=False) # G. C. Greubel, Jun 26 2019

Formula

a(n) = (-1)^n * A077942(n). - G. C. Greubel, Jun 26 2019

a(n) = (-1)^n*Sum_{k=0..(n+1)/2} binomial(n+1-k,2k+1)*(-2)^k, n>=0. - Taras Goy, Apr 15 2020