A075298 Inverted (definition in A075193) generalized tribonacci numbers A001644.

1, 1, -5, 5, 1, -11, 15, -3, -23, 41, -21, -43, 105, -83, -65, 253, -271, -47, 571, -795, 177, 1189, -2161, 1149, 2201, -5511, 4459, 3253, -13223, 14429, 2047, -29699, 42081, -10335, -61445, 113861, -62751, -112555, 289167, -239363, -162359, 690889, -767893, -85355, 1544137, -2226675, 597183, 3173629

Offset: 0

Author

Mario Catalani (mario.catalani(AT)unito.it), Sep 13 2002

Keywords

• easy
• sign

Comments

a(n) = -C(n+1), C(n)=reflected generalized tribonacci numbers A073145.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..5000
• Curtis Cooper, S. Miller, Peter J. C. Moses, M. Sahin, and T. Thanatipanonda, On Identities of Ruggles, Horadam, Howard, and Young, Preprint 2016.
• Index entries for linear recurrences with constant coefficients, signature (-1,-1,1).

Crossrefs

Cf. A001644, A073145, A075193.

Programs

GAP

a:=[1,1,-5];; for n in [4..50] do a[n]:=-a[n-1]-a[n-2]+a[n-3]; od; a; # G. C. Greubel, Apr 09 2019

Magma

R:=PowerSeriesRing(Integers(), 50); Coefficients(R!( (1+2*x-3*x^2)/(1+x+x^2-x^3) )); // G. C. Greubel, Apr 09 2019

Mathematica

CoefficientList[Series[(1+2x-3x^2)/(1+x+x^2-x^3), {x, 0, 50}], x]

PARI

my(x='x+O('x^50)); Vec((1+2*x-3*x^2)/(1+x+x^2-x^3)) \\ G. C. Greubel, Apr 09 2019

Sage

((1+2*x-3*x^2)/(1+x+x^2-x^3)).series(x, 50).coefficients(x, sparse=False) # G. C. Greubel, Apr 09 2019

Formula

a(n) = -a(n-1) - a(n-2) + a(n-3), a(0)=1, a(1)=1, a(2)=-5.

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

a(n) = A078046(n) + 3*A078046(n-1). - R. J. Mathar, Sep 20 2020