A155630 a(n) = 9^n-4^n+1^n.

1, 6, 66, 666, 6306, 58026, 527346, 4766586, 42981186, 387158346, 3485735826, 31376865306, 282412759266, 2541798719466, 22876524019506, 205890058352826, 1853015893884546, 16677164519797386, 150094566577522386

Offset: 0

Author

Mohammad K. Azarian, Jan 30 2009

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (14,-49,36).

Crossrefs

Cf. A155596, A155597, A155598, A155599, A155600, A155601, A155622, A155623, A155624, A155625, A155626, A155627, A155628, A155629.

Programs

Mathematica

Table[9^n-4^n+1,{n,0,20}] (* or *) LinearRecurrence[{14,-49,36},{1,6,66},20] (* Harvey P. Dale, Aug 08 2019 *)

PARI

a(n)=9^n-4^n+1 \\ Charles R Greathouse IV, Sep 24 2015

Formula

G.f.: 1/(1-9*x)-1/(1-4*x)+1/(1-x). E.g.f.: e^(9*x)-e^(4*x)+e^x.

a(n) = 13*a(n-1)-36*a(n-2)+24 with a(0)=1, a(1)=6. - Vincenzo Librandi, Jul 21 2010