A165324 a(0)=1, a(1)=9, a(n)= 19*a(n-1)-81*a(n-2) for n>1.

1, 9, 90, 981, 11349, 136170, 1667961, 20661489, 257463450, 3218224941, 40291734429, 504866733930, 6328837455921, 79353706214169, 995084584139610, 12478956895304901, 156498329695484709, 1962672755694512490

Offset: 0

Author

Philippe Deléham, Sep 14 2009

Keywords

• nonn

Comments

a(n)/a(n-1) tends to (19+sqrt(37))/2 = 12.5413812...

Links

• Index entries for linear recurrences with constant coefficients, signature (19,-81).

Programs

Mathematica

LinearRecurrence[{19,-81},{1,9},20] (* Harvey P. Dale, Nov 20 2020 *)

Formula

G.f.: (1-10x)/(1-19x+81x^2). a(n)= Sum_{k, 0<=k<=n}A165253(n,k)*9^(n-k).

a(n) = ((37-sqrt(37))*(19+sqrt(37))^n+(37+sqrt(37))*(19-sqrt(37))^n)/(74*2^n). [From Klaus Brockhaus, Sep 28 2009]