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a(n) = 5^n - 3^n - 2^n.
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%I #31 Sep 08 2022 08:45:32

%S -1,0,12,90,528,2850,14832,75810,383808,1932930,9705552,48648930,

%T 243605088,1219100610,6098716272,30503196450,152544778368,

%U 762810181890,3814309582992,19072323542370,95363943807648,476826695752770,2384154405761712,11920834803510690,59604362329076928,298022376554789250

%N a(n) = 5^n - 3^n - 2^n.

%C Essentially the same as A130072. - _Zak Seidov_, Oct 03 2011

%H G. C. Greubel, <a href="/A135158/b135158.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (10,-31,30).

%F G.f.: ( 1+19*x^2-10*x ) / ( (3*x-1)*(2*x-1)*(5*x-1) ).

%F a(n) = 10*a(n-1) - 31*a(n-2) + 30*a(n-3). - _Zak Seidov_, Oct 03 2011

%F E.g.f.: exp(5*x) - exp(3*x) - exp(2*x). - _G. C. Greubel_, Sep 30 2016

%e a(4) = 528 because 5^4 = 625, 3^4 = 81, 2^4 = 16 and 625 - 81 - 16 = 528.

%p A135158:=n->5^n-3^n-2^n; seq(A135158(n), n=0..30); # _Wesley Ivan Hurt_, Feb 26 2014

%t lst={};Do[p=5^n-3^n-2^n;AppendTo[lst, p], {n, 0, 7^2}];lst (* _Vladimir Joseph Stephan Orlovsky_, Aug 19 2008 *)

%t LinearRecurrence[{10,-31,30}, {-1, 0, 12}, 25] (* or *) Table[5^n - 3^n - 2^n, {n,0,25}] (* _G. C. Greubel_, Sep 30 2016 *)

%o (Magma)[5^n-3^n-2^n: n in [0..50]] - _Vincenzo Librandi_, Dec 15 2010

%o (PARI) a(n)=5^n-3^n-2^n \\ _Charles R Greathouse IV_, Oct 07 2015

%Y Cf. A000079, A000244, A000351, A001047, A130072.

%K easy,sign

%O 0,3

%A _Omar E. Pol_, Nov 21 2007

%E More terms from _Vincenzo Librandi_, Dec 15 2010