A155626 a(n) = 5^n-4^n+1.

1, 2, 10, 62, 370, 2102, 11530, 61742, 325090, 1690982, 8717050, 44633822, 227363410, 1153594262, 5835080170, 29443836302, 148292923330, 745759583942, 3745977788890, 18798608421182, 94267920012850, 472439111692022

Offset: 0

Author

Mohammad K. Azarian, Jan 29 2009

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (10,-29,20).

Crossrefs

Cf. A054401, which is essentially a(n) - 2. Also A155588, A155589, A155590, A155592, A155593, A155594, A155595, A155596, A155597, A155598, A155599, A155600, A155601, A155622, A155623, A155624, A155625.

Programs

Mathematica

Table[5^n-4^n+1,{n,0,40}] (* Vladimir Joseph Stephan Orlovsky, Feb 15 2011*)
LinearRecurrence[{10,-29,20},{1,2,10},30] (* Harvey P. Dale, Oct 11 2023 *)

PARI

a(n)=5^n-4^n+1 \\ Charles R Greathouse IV, Jun 11 2015

Formula

G.f.: 1/(1-5*x)-1/(1-4*x)+1/(1-x).

E.g.f.: e^(5*x)-e^(4*x)+e^x.

a(n) = 9*a(n-1)-20*a(n-2)+12 with a(0)=1, a(1)=2. - Vincenzo Librandi, Jul 21 2010

a(n) = 10*a(n-1)-29*a(n-2)+20*a(n-3). - Wesley Ivan Hurt, Jun 07 2021