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).
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
KEYWORD
easy,sign
AUTHOR
Mario Catalani (mario.catalani(AT)unito.it), Sep 13 2002
STATUS
approved