A077951 Expansion of 1/(1-x+x^2-2*x^3).

1, 1, 0, 1, 3, 2, 1, 5, 8, 5, 7, 18, 21, 17, 32, 57, 59, 66, 121, 173, 184, 253, 415, 530, 621, 921, 1360, 1681, 2163, 3202, 4401, 5525, 7528, 10805, 14327, 18578, 25861, 35937, 47232, 63017, 87659, 119106, 157481, 213693, 294424, 395693, 528655, 721810, 984541, 1320041

Offset: 0

Author

N. J. A. Sloane, Nov 17 2002

Keywords

• nonn
• easy

Links

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

Programs

GAP

a:=[1,1,0];; for n in [4..50] do a[n]:= a[n-1]-a[n-2]+2*a[n-3]; od; a; # G. C. Greubel, Jul 03 2019

Magma

R:=PowerSeriesRing(Integers(), 50); Coefficients(R!( 1/(1-x+x^2-2*x^3) )); // G. C. Greubel, Jul 03 2019

Mathematica

LinearRecurrence[{1, -1, 2}, {1, 1, 0}, 60] (* Vladimir Joseph Stephan Orlovsky, Feb 23 2012 *)
CoefficientList[Series[1/(1-x+x^2-2*x^3), {x,0,50}], x] (* G. C. Greubel, Jul 03 2019 *)

PARI

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

Sage

(1/(1-x+x^2-2*x^3)).series(x, 50).coefficients(x, sparse=False) # G. C. Greubel, Jul 03 2019