A333344 a(n) = 11*a(n-1) - 9*a(n-2) starting a(0)=1, a(1)=10.

1, 10, 101, 1021, 10322, 104353, 1054985, 10665658, 107827373, 1090110181, 11020765634, 111417430345, 1126404843089, 11387696400874, 115127016821813, 1163907917432077, 11766843940356530, 118960112087033137, 1202659637494155737

Offset: 0

Author

Kevin Ryde, Mar 15 2020

Keywords

• nonn
• easy

Comments

First differences of A190872.

Links

• Kevin Ryde, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (11,-9).

Crossrefs

Cf. A333345 (growth power), A190872 (partial sums), A147841, A333347.

Programs

Mathematica

LinearRecurrence[{11, -9}, {1, 10}, 20] (* Amiram Eldar, Mar 15 2020 *)

PARI

a(n) = polcoeff(lift(('x-1)*Mod('x,'x^2-11*'x+9)^n), 1);

Formula

a(n) = A190872(n+1) - A190872(n) = A190872(n) + A147841(n).

G.f.: (1 - x)/(1 - 11*x + 9*x^2).

E.g.f.: exp(11*x/2)*(85*cosh(sqrt(85)*x/2) + 9*sqrt(85)*sinh(sqrt(85)*x/2))/85. - Stefano Spezia, Mar 03 2023