A014923 a(1) = 1, a(n) = n*9^(n-1) + a(n-1).

1, 19, 262, 3178, 35983, 390277, 4110364, 42374116, 429794605, 4303999495, 42658627906, 419231343214, 4090815317467, 39676936914073, 382828823738488, 3677086937252872, 35178430147734169, 335367700741732411, 3187165771384715710, 30204200124844557490, 285515174765040062311

Offset: 1

Author

Olivier Gérard

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (19,-99,81).

Programs

Magma

I:=[1, 19]; [n le 2 select I[n] else 18*Self(n-1) - 81*Self(n-2) + 1: n in [1..30]]; // Vincenzo Librandi, Oct 23 2012

Mathematica

CoefficientList[Series[1/((1 - x)(1 - 9*x)^2), {x, 0, 40}], x] (* Vincenzo Librandi, Oct 23 2012 *)

PARI

Vec(x/((1 - x)*(1 - 9*x)^2) + O(x^30)) \\ Jinyuan Wang, Mar 11 2020

Formula

From Vincenzo Librandi, Oct 23 2012: (Start)

a(n) = 18*a(n-1) - 81*a(n-2) + 1, a(1)=1, a(2)=19.

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

From Elmo R. Oliveira, May 15 2025: (Start)

E.g.f.: exp(x)*(1 + exp(8*x)*(72*x - 1))/64.

a(n) = (9^n*(8*n - 1) + 1)/64.

a(n) = 19*a(n-1) - 99*a(n-2) + 81*a(n-3) for n >= 4. (End)