A077976 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

• 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

Partial sums give: A077909.

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, Jun 25 2019

Magma

R:=PowerSeriesRing(Integers(), 50); Coefficients(R!( 1/(1+x+x^2+2*x^3) )); // G. C. Greubel, Jun 25 2019

Mathematica

LinearRecurrence[{-1, -1, -2}, {1, -1, 0}, 50] (* Vladimir Joseph Stephan Orlovsky, Feb 24 2012 *)

PARI

my(x='x+O('x^50)); Vec(1/(1+x+x^2+2*x^3)) \\ G. C. Greubel, Jun 25 2019

Sage

(1/(1+x+x^2+2*x^3)).series(x, 50).coefficients(x, sparse=False) # G. C. Greubel, Jun 25 2019