A155651 a(n) = 8^n-6^n+1^n.

1, 3, 29, 297, 2801, 24993, 215489, 1817217, 15097601, 124140033, 1013275649, 8227137537, 66542694401, 536695119873, 4319682347009, 34714187104257, 278653866803201, 2234873154240513, 17912838552813569, 143505828335845377

Offset: 0

Author

Mohammad K. Azarian, Jan 31 2009

Keywords

• nonn
• easy

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (15,-62,48).

Crossrefs

Cf. A155628, A155629, A155630, A155631, A155632, A155633, A155634, A155635, A155636, A155637, A155638, A155639, A155640, A155641, A155642, A155643, A155644, A155645, A155646, A155647, A155648, A155649, A155650.

Programs

Magma

[8^n-6^n+1 : n in [0..30]]; // Wesley Ivan Hurt, Jul 07 2025

Mathematica

Table[8^n-6^n+1,{n,0,20}] (* or *) LinearRecurrence[{15,-62,48},{1,3,29},20] (* Harvey P. Dale, Jul 12 2020 *)

PARI

a(n)=8^n-6^n+1 \\ Charles R Greathouse IV, Jun 11 2015

Formula

G.f.: 1/(1-8*x)-1/(1-6*x)+1/(1-x).

E.g.f.: e^(8*x)-e^(6*x)+e^x.

a(n)=14*a(n-1)-48*a(n-2)+35 with a(0)=1, a(1)=3. - Vincenzo Librandi, Jul 21 2010