A086580 a(n) = 9*(10^n - 1).

0, 81, 891, 8991, 89991, 899991, 8999991, 89999991, 899999991, 8999999991, 89999999991, 899999999991, 8999999999991, 89999999999991, 899999999999991, 8999999999999991, 89999999999999991, 899999999999999991, 8999999999999999991, 89999999999999999991, 899999999999999999991

Offset: 0

Author

Ray Chandler, Jul 22 2003

Keywords

• nonn
• base
• easy

Comments

Original definition: a(n) = k where R(k+9) = 9.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..990
• Index entries for linear recurrences with constant coefficients, signature (11,-10).

Crossrefs

Cf. A002275, A004086 (R(n)), A086573.

One of family of sequences of form a(n) = k, where R(k+m) = m, m=1 to 9; m=1: A002283, m=2: A086573, m=3: A086574, m=4: A086575, m=5: A086576, m=6: A086577, m=7: A086578, m=8: A086579, m=9: A086580.

Programs

Magma

[9*(10^n -1): n in [0..30]]; // G. C. Greubel, Jul 07 2023

Mathematica

Table[9*(10^n-1), {n,0,30}] (* G. C. Greubel, Jul 07 2023 *)

SageMath

A086580=BinaryRecurrenceSequence(11,-10,0,81)
[A086580(n) for n in range(30)] # G. C. Greubel, Jul 07 2023

Formula

a(n) = 9*9*A002275(n) = 9*A002283(n).

R(a(n)) = A086573(n).

From Chai Wah Wu, Jul 08 2016: (Start)

a(n) = 11*a(n-1) - 10*a(n-2) for n > 1.

G.f.: 81*x/((1 - x)*(1 - 10*x)). (End)

E.g.f.: 9*exp(x)*(exp(9*x) - 1). - Elmo R. Oliveira, Sep 12 2024

Extensions

Name edited by Jinyuan Wang, Aug 04 2021