OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (18,-104,192).
FORMULA
a(n) = 2*4^n -9*6^n +8*8^n. - R. J. Mathar, Jun 29 2013
From Vincenzo Librandi, Jul 02 2013: (Start)
a(n) = 18*a(n-1) - 104*a(n-2) + 192*a(n-3) for n > 2.
a(n) = 14*a(n-1) - 48*a(n-2) + 4^n. (End)
E.g.f.: exp(4*x)*(2 - 9*exp(2*x) + 8*exp(4*x)). - Stefano Spezia, Jun 04 2024
MATHEMATICA
CoefficientList[Series[1 / ((1 - 4 x) (1 - 6 x) (1 - 8 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 02 2013 *)
PROG
(PARI) Vec(1/((1-4*x)*(1-6*x)*(1-8*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012
(Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-4*x)*(1-6*x)*(1-8*x)))); /* or */ I:=[1, 18, 220]; [n le 3 select I[n] else 18*Self(n-1)-104*Self(n-2)+192*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Jul 02 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved