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

0,3

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).

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

Mathematica

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

Prog

(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
(Magma) R<x>:=PowerSeriesRing(Integers(), 50); Coefficients(R!( (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
(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

Crossrefs

Cf. A001644, A073145, A075193.

Sequence in context: A011094 A319569 A204005 * A370262 A060058 A092766

Adjacent sequences: A075295 A075296 A075297 * A075299 A075300 A075301

Keyword

easy,sign

Author

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

Status

approved