A155602 4^n + 3^n - 1.

1, 6, 24, 90, 336, 1266, 4824, 18570, 72096, 281826, 1107624, 4371450, 17308656, 68703186, 273218424, 1088090730, 4338014016, 17309009346, 69106897224, 276040168410, 1102998412176, 4408506864306, 17623567104024, 70462887356490

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (8,-19,12).

Formula

G.f.: 1/(1-4*x)+1/(1-3*x)-1/(1-x). E.g.f.: e^(4*x)+e^(3*x)-e^x.

a(n) = 7*a(n-1) - 12*a(n-2) -6, n>1 - Gary Detlefs, Jun 21 2010

a(n) = 8*a(n-1) - 19*a(n-2) + 12*a(n-3), n>2, a(0)=1, a(1)=6, a(2)=24. - L. Edson Jeffery, Oct 17 2012

a(n) = A074605(n)-1. - R. J. Mathar, Mar 10 2022

Mathematica

Table[4^n + 3^n - 1, {n, 0, 50}] (* Vincenzo Librandi, Oct 17 2012 *)
LinearRecurrence[{8, -19, 12}, {1, 6, 24}, 30] (* Harvey P. Dale, Apr 28 2018 *)

Prog

(Magma) [(4^n + 3^n - 1): n in [0..30]]; // Vincenzo Librandi, Oct 17 2012
(PARI) a(n)=4^n+3^n-1 \\ Charles R Greathouse IV, Sep 24 2015

Crossrefs

Cf. A074501, A020515, A155588, A155590, A155592-A155594, A155596-A155601.

Sequence in context: A002919 A006780 A001352 * A179716 A326755 A365978

Adjacent sequences: A155599 A155600 A155601 * A155603 A155604 A155605

Keyword

nonn,easy

Author

Mohammad K. Azarian, Jan 25 2009

Status

approved