A155617 6^n + 4^n - 1.

1, 9, 51, 279, 1551, 8799, 50751, 296319, 1745151, 10339839, 61514751, 366991359, 2193559551, 13127802879, 78632599551, 471258726399, 2825404874751, 16943839313919, 101628676145151, 609634617917439, 3657257951690751

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

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

Formula

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, n>1 - Gary Detlefs, Jun 21 2010

a(n) = 11*a(n-1)-34*a(n-2)+24*a(n-3). - Vincenzo Librandi, Feb 16 2013

Mathematica

Table[(6^n + 4^n - 1^n), {n, 0, 30}] (* Vincenzo Librandi, Feb 16 2013 *)
LinearRecurrence[{11, -34, 24}, {1, 9, 51}, 30] (* Harvey P. Dale, Mar 30 2019 *)

Prog

(Magma) [6^n+4^n-1: n in [0..20]]; /* or */ I:=[1, 9, 51]; [n le 3 select I[n] else 11*Self(n-1)-34*Self(n-2)+24*Self(n-3): n in [1..25]]; // Vincenzo Librandi, Feb 16 2013
(PARI) a(n)=6^n+4^n-1 \\ Charles R Greathouse IV, Oct 16 2015

Crossrefs

Cf. A155588, A155599, A155607, A155608, A155609, A155610, A155611, A155612, A155613, A155614, A155615, A155616.

Sequence in context: A125319 A080621 A027218 * A126477 A275861 A210054

Adjacent sequences: A155614 A155615 A155616 * A155618 A155619 A155620

Keyword

nonn,easy

Author

Mohammad K. Azarian, Jan 27 2009

Status

approved