A155623 a(n) = 11^n + 3^n - 1.

1, 13, 129, 1357, 14721, 161293, 1772289, 19489357, 214365441, 2357967373, 25937483649, 285311847757, 3138428908161, 34522713738253, 379749838366209, 4177248183764557, 45949729906618881, 505447028628433933

Offset: 0

Author

Mohammad K. Azarian, Jan 29 2009

Keywords

• nonn
• easy

Comments

a^n+b^n-1^n=(a+b)*a(n-1)-(a*b)*a(n-2)-(a-1)*(b-1) - Vincenzo Librandi, Jul 21 2010

Links

• Index entries for linear recurrences with constant coefficients, signature (15,-47,33).

Crossrefs

Cf. A155588, A155589, A155590, A155592, A155593, A155594, A155595, A155596, A155597, A155598, A155599, A155600, A155601, A155622.

Programs

Mathematica

LinearRecurrence[{15,-47,33},{1,13,129},20] (* Harvey P. Dale, Jan 14 2015 *)

PARI

a(n)=11^n+3^n-1 \\ Charles R Greathouse IV, Jun 11 2015

Formula

G.f.: 1/(1 - 11*x) + 1/(1 - 3*x) - 1/(1 - x).

E.g.f.: exp(11*x) + exp(3*x) - exp(x).

a(n) = 14*a(n-1) - 33*a(n-2) - 20 for n>1, a(0)=1, a(1)=13 - Vincenzo Librandi, Jul 21 2010