A077942 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. A077989.

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, Aug 05 2019

Magma

R:=PowerSeriesRing(Integers(), 40); Coefficients(R!( 1/(1-2*x+x^2+2*x^3) )); // G. C. Greubel, Aug 05 2019

Maple

seq(coeff(series(1/(1-2*x+x^2+2*x^3), x, n+1), x, n), n = 0..40); # G. C. Greubel, Aug 05 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, Aug 05 2019 *)

PARI

Vec(1/(1-2*x+x^2+2*x^3)+O(x^40)) \\ Charles R Greathouse IV, Sep 27 2012

Sage

(1/(1-2*x+x^2+2*x^3)).series(x, 40).coefficients(x, sparse=False) # G. C. Greubel, Aug 05 2019

Formula

a(n) = (-1)^n * A077989(n). - G. C. Greubel, Aug 05 2019

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