A190543 a(n) = 8^n - 3^n.

0, 5, 55, 485, 4015, 32525, 261415, 2094965, 16770655, 134198045, 1073682775, 8589757445, 68718945295, 549754219565, 4398041728135, 35184357739925, 281474933663935, 2251799684545085, 18014398122061495, 144115186913594405, 1152921501120062575, 9223372026394422605

Offset: 0

Author

Vincenzo Librandi, Jun 02 2011

Keywords

• nonn
• easy

Comments

Length-n words from letters {1, 2, ..., 8} with at least one letter greater than 3. - Joerg Arndt, Jun 02 2011

All terms are odd multiples of 5, since the powers of 8 mod 10 are 8, 4, 2, 6, ... and the powers of 3 mod 10 are 3, 9, 7, 1, ... - Alonso del Arte, Feb 25 2014

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..300
• Feryal Alayont and Evan Henning, Edge Covers of Caterpillars, Cycles with Pendants, and Spider Graphs, J. Int. Seq. (2023) Vol. 26, Art. 23.9.4.
• Index entries for linear recurrences with constant coefficients, signature (11,-24).

Crossrefs

Cf. A000244, A001018, A016140, A016177.

Programs

Magma

[8^n - 3^n: n in [0..30]];

Maple

A190543:=n->8^n - 3^n; seq(A190543(n), n=0..20); # Wesley Ivan Hurt, Feb 26 2014

Mathematica

Table[8^n - 3^n, {n, 0, 19}] (* Alonso del Arte, Feb 25 2014 *)
CoefficientList[Series[5 x/((1 - 3 x) (1 - 8 x)), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 05 2014 *)

PARI

a(n)=8^n-3^n \\ Charles R Greathouse IV, Jun 02 2011

Formula

a(n) = 11*a(n-1) - 24*a(n-2).

a(n) = A001018(n) - A000244(n). - Michel Marcus, Feb 26 2014

From Vincenzo Librandi, Oct 05 2014: (Start)

G.f.: 5*x/((1-3*x)*(1-8*x)).

a(n+1) = 5*A016140(n). (End)

E.g.f.: 2*exp(11*x/2)*sinh(5*x/2). - Elmo R. Oliveira, Mar 31 2025