A155610 5^n - 3^n + 1.

1, 3, 17, 99, 545, 2883, 14897, 75939, 384065, 1933443, 9706577, 48650979, 243609185, 1219108803, 6098732657, 30503229219, 152544843905, 762810312963, 3814309845137, 19072324066659, 95363944856225, 476826697849923

Offset: 0

Author

Mohammad K. Azarian, Jan 26 2009

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (9,-23,15).

Crossrefs

Cf. A155596, A155597, A155598, A155599, A155600, A155601, A155602, A155603, A155604, A155605, A155606, A155607, A155608, A155609.

Programs

Mathematica

Table[5^n-3^n+1,{n,0,30}] (* or *) LinearRecurrence[{9,-23,15},{1,3,17},31] (* Harvey P. Dale, Jan 06 2012 *)

PARI

a(n)=5^n-3^n+1 \\ Charles R Greathouse IV, Oct 07 2015

Formula

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

E.g.f.: e^(5*x)-e^(3*x)+e^x.

a(n) = 8*a(n-1)-15*a(n-2)+8 with a(0)=1, a(1)=3. - Vincenzo Librandi, Jul 21 2010

a(0)=1, a(1)=3, a(2)=17, a(n)=9*a(n-1)-23*a(n-2)+15*a(n-3). - Harvey P. Dale, Jan 06 2012