A155667 a(n) = 10^n-8^n+1.

1, 3, 37, 489, 5905, 67233, 737857, 7902849, 83222785, 865782273, 8926258177, 91410065409, 931280523265, 9450244186113, 95601953488897, 964815627911169, 9718525023289345, 97748200186314753, 981985601490518017

Offset: 0

Author

Mohammad K. Azarian, Jan 31 2009

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (19,-98,80).

Crossrefs

Cf. A155646, A155647, A155648, A155649, A155650, A155651, A155652, A155653, A155654, A155655, A155656, A155657, A155658, A155659, A155660, A155661, A155662, A155663, A155664, A155665, A155666.

Programs

Mathematica

Table[10^n - 8^n + 1, {n, 0, 25}] (* Paolo Xausa, Aug 02 2024 *)

PARI

a(n)=10^n-8^n+1 \\ Charles R Greathouse IV, Jun 11 2015

Formula

G.f.: 1/(1-10*x)-1/(1-8*x)+1/(1-x).

E.g.f.: e^(10*x)-e^(8*x)+e^x.

a(n) = 18*a(n-1)-80*a(n-2)+63 with a(0) = 1, a(1) = 3. - Vincenzo Librandi, Jul 21 2010

a(n) = 19*a(n-1) - 98*a(n-2) + 80*a(n-3). - Wesley Ivan Hurt, Apr 18 2023