A155641 8^n-5^n+1^n.

1, 4, 40, 388, 3472, 29644, 246520, 2019028, 16386592, 132264604, 1063976200, 8541106468, 68475336112, 548535110764, 4391942995480, 35153854510708, 281322388820032, 2251036874232124, 18010583812216360, 144096114589527748

Offset: 0

Author

Mohammad K. Azarian, Jan 30 2009

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (14,-53,40).

Crossrefs

Cf. A155624, A155625, A155626, A155627, A155628, A155629, A155630, A155631, A155632, A155633, A155634, A155635, A155636, A155637, A155638, A155639, A155640.

Programs

Mathematica

Table[8^n-5^n+1^n,{n,0,20}] (* or *) LinearRecurrence[{14,-53,40},{1,4,40},20] (* Harvey P. Dale, May 08 2018 *)

PARI

a(n)=8^n-5^n+1 \\ Charles R Greathouse IV, Jun 11 2015

Formula

G.f.: 1/(1-8*x)-1/(1-5*x)+1/(1-x). E.g.f.: e^(8*x)-e^(5*x)+e^x.

a(n)=13*a(n-1)-40*a(n-2)+28 with a(0)=1, a(1)=4 - Vincenzo Librandi, Jul 21 2010