A190540 a(n) = 7^n - 2^n.

0, 5, 45, 335, 2385, 16775, 117585, 823415, 5764545, 40353095, 282474225, 1977324695, 13841283105, 96889002215, 678223056465, 4747561477175, 33232930504065, 232630513856135, 1628413597648305, 11398895184848855, 79792266296563425, 558545864081186855, 3909821048578793745

Offset: 0

Author

Vincenzo Librandi, Jun 02 2011

Keywords

• nonn
• easy

Comments

Length-n words from letters {1,2,...,7} with at least one letter >2. [Joerg Arndt, Jun 02 2011]

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..300
• Index entries for linear recurrences with constant coefficients, signature (9,-14).

Crossrefs

Cf. A016130, A016169, A121213.

Programs

Magma

[7^n -2^n: n in [0..30]];

Mathematica

CoefficientList[Series[5 x/((1 - 2 x) (1 - 7 x)), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 04 2014 *)

PARI

a(n)=7^n-1<Charles R Greathouse IV, Jun 08 2011

Formula

a(n) = 9*a(n-1) - 14*a(n-2).

G.f.: 5*x/((1-2*x)*(1-7*x)). - Vincenzo Librandi, Oct 04 2014

a(n) = 5*A016130(n-1). - R. J. Mathar, Mar 10 2022

E.g.f.: exp(2*x)*(exp(5*x) - 1). - Elmo R. Oliveira, Sep 10 2024