A062396 a(n) = 9^n + 1.

2, 10, 82, 730, 6562, 59050, 531442, 4782970, 43046722, 387420490, 3486784402, 31381059610, 282429536482, 2541865828330, 22876792454962, 205891132094650, 1853020188851842, 16677181699666570, 150094635296999122

Offset: 0

Author

Henry Bottomley, Jun 22 2001

Keywords

• easy
• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (10,-9).

Crossrefs

Cf. A054977, A007395, A000051, A034472, A052539, A034474, A062394, A034491, A062395, A062397, A007689, A063376, A063481, A074600-A074624, A034524, A178248, A228081 for numbers one more than powers.

Programs

Magma

[9^n + 1: n in [0..35]]; // Vincenzo Librandi, Apr 30 2011

Mathematica

Table[9^n + 1, {n, 0, 20}]
LinearRecurrence[{10,-9},{2,10},20] (* Harvey P. Dale, May 30 2013 *)

PARI

a(n)=9^n+1 \\ Charles R Greathouse IV, Sep 24 2015

Formula

a(n) = 9*a(n-1) - 8 = A001019(n) + 1 = 10*a(n-1) - 9*a(n-2).

From Mohammad K. Azarian, Jan 02 2009: (Start)

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

E.g.f.: e^x + e^(9*x). (End)