A078004 Expansion of (1-x)/(1-2*x+2*x^2+x^3).

1, 1, 0, -3, -7, -8, 1, 25, 56, 61, -15, -208, -447, -463, 176, 1725, 3561, 3496, -1855, -14263, -28312, -26243, 18401, 117600, 224641, 195681, -175520, -967043, -1778727, -1447848, 1628801, 7932025, 14054296, 10615741, -14809135, -64904048, -110805567, -76993903, 132527376

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,-2,-1).

Programs

GAP

a:=[1,1,0];; for n in [4..40] do a[n]:=2*a[n-1]-2*a[n-2]-a[n-3]; od; a; # G. C. Greubel, Jun 27 2019

Magma

R:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1-x)/( 1-2*x+2*x^2+x^3) )); // G. C. Greubel, Jun 27 2019

Mathematica

LinearRecurrence[{2,-2,-1}, {1,1,0}, 40] (* or *) CoefficientList[ Series[(1-x)/(1-2*x+2*x^2+x^3), {x,0,40}], x] (* G. C. Greubel, Jun 27 2019 *)

PARI

my(x='x+O('x^40)); Vec((1-x)/(1-2*x+2*x^2+x^3)) \\ G. C. Greubel, Jun 27 2019

Sage

((1-x)/(1-2*x+2*x^2+x^3)).series(x, 40).coefficients(x, sparse=False) # G. C. Greubel, Jun 27 2019

Formula

G.f.: (1-x)/(1-2*x+2*x^2+x^3).

a(n) = 2*a(n-1) - 2*a(n-2) - a(n-3). - Wesley Ivan Hurt, Jul 29 2022