OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..500
Index entries for linear recurrences with constant coefficients, signature (-8, 9).
FORMULA
a(n) = -8*a(n-1) + 9*a(n-2), a(0)=1, a(1)=9.
a(n) = (-9)*a(n-1) + 18 for n>=1, with a(0)=1.
G.f.: (1+17x)/(1+8x-9x^2).
a(n) = Sum_{0<=k<=n} A112555(n,k)*8^(n-k).
E.g.f.: (1/5)*(9*exp(x) - 4*exp(-9*x)). - G. C. Greubel, Apr 07 2016
MATHEMATICA
Table[9/5 (1+4(-9)^(n-1)), {n, 0, 20}] (* or *) LinearRecurrence[{-8, 9}, {1, 9}, 20] (* Harvey P. Dale, Nov 24 2011 *)
PROG
(PARI) x='x+O('x^99); Vec((1+17*x)/(1+8*x-9*x^2)) \\ Altug Alkan, Apr 07 2016
(PARI) a(n) = (9-4*(-9)^n)/5 \\ Charles R Greathouse IV, Apr 07 2016
CROSSREFS
KEYWORD
easy,sign
AUTHOR
Philippe Deléham, Sep 26 2009
STATUS
approved