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4^n + 3^n - 1.
13

%I #27 Sep 08 2022 08:45:40

%S 1,6,24,90,336,1266,4824,18570,72096,281826,1107624,4371450,17308656,

%T 68703186,273218424,1088090730,4338014016,17309009346,69106897224,

%U 276040168410,1102998412176,4408506864306,17623567104024,70462887356490

%N 4^n + 3^n - 1.

%H Vincenzo Librandi, <a href="/A155602/b155602.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (8,-19,12).

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

%F a(n) = 7*a(n-1) - 12*a(n-2) -6, n>1 - _Gary Detlefs_, Jun 21 2010

%F 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

%F a(n) = A074605(n)-1. - _R. J. Mathar_, Mar 10 2022

%t Table[4^n + 3^n - 1, {n, 0, 50}] (* _Vincenzo Librandi_, Oct 17 2012 *)

%t LinearRecurrence[{8,-19,12},{1,6,24},30] (* _Harvey P. Dale_, Apr 28 2018 *)

%o (Magma) [(4^n + 3^n - 1): n in [0..30]]; // _Vincenzo Librandi_, Oct 17 2012

%o (PARI) a(n)=4^n+3^n-1 \\ _Charles R Greathouse IV_, Sep 24 2015

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

%K nonn,easy

%O 0,2

%A _Mohammad K. Azarian_, Jan 25 2009