A103460 a(n) = 9^n + 1 - 0^n.

1, 10, 82, 730, 6562, 59050, 531442, 4782970, 43046722, 387420490, 3486784402, 31381059610, 282429536482, 2541865828330, 22876792454962, 205891132094650, 1853020188851842, 16677181699666570, 150094635296999122

Offset: 0

Author

Paul Barry, Feb 07 2005

Keywords

• easy
• nonn

Comments

a(n)^3 is palindromic in base 9 (1_9, 1331_9, 1030301_9, 1003003001_9, ...).

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Patrick De Geest, World!Of Numbers
• Index entries for linear recurrences with constant coefficients, signature (10, -9).

Crossrefs

Cf. A046233, A062396.

Programs

Magma

[1] cat [9^n +1: n in [1..40]]; // G. C. Greubel, Jun 26 2021

Mathematica

Table[9^n + 1 - Boole[n==0], {n,0,40}] (* G. C. Greubel, Jun 26 2021 *)

Sage

[1]+[9^n +1 for n in (1..40)] # G. C. Greubel, Jun 26 2021

Formula

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

a(n) = Sum_{k=0..n} binomial(n, k)*0^(k*(n-k))*9^k.

a(n) = A062396(n), n > 0. - R. J. Mathar, Aug 28 2008

a(n) = 9*a(n-1) - 8, with a(1)=10. - Vincenzo Librandi, Dec 29 2010

E.g.f.: -1 + exp(x) + exp(9*x). - G. C. Greubel, Jun 26 2021