A155622 -id:A155622 - cp's OEIS frontend

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

Mohammad K. Azarian, Jan 29 2009

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

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

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

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

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

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

A155627 a(n) = 6^n - 4^n + 1.

Original entry on oeis.org

1, 3, 21, 153, 1041, 6753, 42561, 263553, 1614081, 9815553, 59417601, 358602753, 2160005121, 12993585153, 78095728641, 469111242753, 2816814940161, 16909479575553, 101491237191681, 609084862103553, 3655058928435201

Offset: 0

Mohammad K. Azarian, Jan 29 2009

Index entries for linear recurrences with constant coefficients, signature (11,-34,24).

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

Table[6^n - 4^n + 1, {n, 0, 25}] (* Paolo Xausa, Jun 26 2024 *)

a(n)=6^n-4^n+1 \\ Charles R Greathouse IV, Jun 11 2015

O.g.f.: 1/(1 - 6*x) - 1/(1 - 4*x) + 1/(1 - x).
E.g.f.: exp(6*x) - exp(4*x) + exp(x).
a(n) = 10*a(n-1)-24*a(n-2)+15 with a(0)=1, a(1)=3 - Vincenzo Librandi, Jul 21 2010

cp's OEIS Frontend

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

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