OFFSET
0,1
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (7,-5,1).
FORMULA
a(n) = 7*a(n-1) - 5*a(n-2) + a(n-3), a(0)=3, a(1)=7, a(2)=39.
G.f.: (3-14*x+5*x^2)/(1-7*x+5*x^2-x^3).
MATHEMATICA
CoefficientList[Series[(3-14*x+5*x^2)/(1-7*x+5*x^2-x^3), {x, 0, 30}], x]
LinearRecurrence[{7, -5, 1}, {3, 7, 39}, 30] (* Harvey P. Dale, Mar 24 2022 *)
PROG
(PARI) my(x='x+O('x^30)); Vec((3-14*x+5*x^2)/(1-7*x+5*x^2-x^3)) \\ G. C. Greubel, Apr 13 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (3-14*x+5*x^2)/(1-7*x+5*x^2-x^3) )); // G. C. Greubel, Apr 13 2019
(Sage) ((3-14*x+5*x^2)/(1-7*x+5*x^2-x^3)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, Apr 13 2019
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Mario Catalani (mario.catalani(AT)unito.it), Aug 24 2002
STATUS
approved