A077913 Expansion of 1/((1-x)*(1+x+2*x^2+x^3)).

1, 0, -1, 1, 2, -2, -2, 5, 2, -9, 1, 16, -8, -24, 25, 32, -57, -31, 114, 6, -202, 77, 322, -273, -447, 672, 496, -1392, -271, 2560, -625, -4223, 2914, 6158, -7762, -7467, 16834, 5863, -32063, 3504, 54760, -29704, -83319, 87968, 108375, -200991, -103726, 397334, 11110, -702051, 282498, 1110495

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 (0,-1,1,1).

Programs

GAP

a:=[1,0,-1,1];; for n in [5..60] do a[n]:=-a[n-2]+a[n-3]+a[n-4]; od; a; # G. C. Greubel, Jul 02 2019

Magma

R:=PowerSeriesRing(Integers(), 60); Coefficients(R!( 1/((1-x)*(1+x+2*x^2+x^3)) )); // G. C. Greubel, Jul 02 2019

Mathematica

LinearRecurrence[{0,-1,1,1}, {1,0,-1,1}, 60] (* or *) CoefficientList[ Series[1/((1-x)*(1+x+2*x^2+x^3)), {x,0,60}], x] (* G. C. Greubel, Jul 02 2019 *)

PARI

my(x='x+O('x^60)); Vec(1/((1-x)*(1+x+2*x^2+x^3))) \\ G. C. Greubel, Jul 02 2019

Sage

(1/((1-x)*(1+x+2*x^2+x^3))).series(x, 60).coefficients(x, sparse=False) # G. C. Greubel, Jul 02 2019

Formula

G.f.: 1-x^2/(U(0)+x^2) where U(k)= 1 + (1+x)*x/( 1 - (1+x)*x/((1+x)*x + 1/U(k+1))) ; (continued fraction, 2-step). - Sergei N. Gladkovskii, Oct 24 2012

5*a(n) = 1 + 4*A077979(n) + 3*A077979(n-1) + A077979(n-2). - R. J. Mathar, Jul 10 2013