A165750 a(n) = (10/11)*(2+9*(-10)^(n-1)).

1, 10, -80, 820, -8180, 81820, -818180, 8181820, -81818180, 818181820, -8181818180, 81818181820, -818181818180, 8181818181820, -81818181818180, 818181818181820, -8181818181818180, 81818181818181820

Offset: 0

Author

Philippe Deléham, Sep 26 2009

Keywords

• easy
• sign

Links

• G. C. Greubel, Table of n, a(n) for n = 0..500
• Index entries for linear recurrences with constant coefficients, signature (-9, 10).

Programs

Mathematica

Table[(10/11)*(2 + 9*(-10)^(n - 1)), {n, 0, 50}] (* or *)
LinearRecurrence[{-9,10}, {1,10}, 50] (* G. C. Greubel, Apr 07 2016 *)

PARI

x='x+O('x^99); Vec((1+19*x)/(1+9*x-10*x^2)) \\ Altug Alkan, Apr 07 2016

Formula

a(n) = -9*a(n-1) + 10*a(n-2), a(0)=1, a(1)=10.

a(n) = (-10)*a(n-1) + 20 for n>=1, a(0)=1.

G.f.: (1+19x)/(1+9x-10x^2).

a(n)= Sum_{0<=k<=n} A112555(n,k)*9^(n-k).

E.g.f.: (1/11)*(20*exp(x) - 9*exp(-10*x)). - G. C. Greubel, Apr 07 2016