A078017 Expansion of (1-x)/(1-x+x^2+2*x^3).

1, 0, -1, -3, -2, 3, 11, 12, -5, -39, -58, -9, 127, 252, 143, -363, -1010, -933, 803, 3756, 4819, -543, -12874, -21969, -8009, 39708, 91655, 67965, -103106, -354381, -387205, 173388, 1269355, 1870377, 254246, -4154841, -8149841, -4503492, 11956031, 32759205, 29810158, -26861109

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 (1,-1,-2).

Crossrefs

Cf. A077952.

Programs

GAP

a:=[1,0,-1];; for n in [4..50] do a[n]:=a[n-1]-a[n-2]-2*a[n-3]; od; a; # G. C. Greubel, Jun 29 2019

Magma

R:=PowerSeriesRing(Integers(), 50); Coefficients(R!( (1-x)/(1-x+x^2+2*x^3) )); // G. C. Greubel, Jun 29 2019

Mathematica

LinearRecurrence[{1,-1,-2}, {1,0,-1}, 50] (* or *) CoefficientList[ Series[(1-x)/(1-x+x^2+2*x^3), {x,0,50}], x] (* G. C. Greubel, Jun 29 2019 *)

PARI

Vec((1-x)/(1-x+x^2+2*x^3)+O(x^50)) \\ Charles R Greathouse IV, Sep 27 2012

Sage

((1-x)/(1-x+x^2+2*x^3)).series(x, 50).coefficients(x, sparse=False) # G. C. Greubel, Jun 29 2019

Formula

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

a(n) = A077952(n) - A077952(n-1). - G. C. Greubel, Jun 29 2019