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a(n) = 6^n - 6*n.
2

%I #35 Sep 11 2024 10:57:44

%S 1,0,24,198,1272,7746,46620,279894,1679568,10077642,60466116,

%T 362796990,2176782264,13060693938,78364164012,470184984486,

%U 2821109907360,16926659444634,101559956668308,609359740010382,3656158440062856,21936950640377730,131621703842267004,789730223053602678

%N a(n) = 6^n - 6*n.

%H Vincenzo Librandi, <a href="/A198396/b198396.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 (8,-13,6).

%F a(n) = 8*a(n-1) - 13*a(n-2) + 6*a(n-3) for n > 2.

%F G.f.: (1-8*x+37*x^2)/((1-6*x)*(1-x)^2). - _Vincenzo Librandi_, Jan 04 2013

%F E.g.f.: exp(x)*(exp(5*x) - 6*x). - _Elmo R. Oliveira_, Sep 10 2024

%t CoefficientList[Series[(1 - 8*x + 37*x^2)/((1 - 6*x)*(1 -x)^2), {x, 0, 30}], x] (* _Vincenzo Librandi_, Jan 04 2013 *)

%t Table[6^n-6n,{n,0,30}] (* or *) LinearRecurrence[{8,-13,6},{1,0,24},30] (* _Harvey P. Dale_, Jul 25 2019 *)

%o (Magma) [6^n-6*n: n in [0..25]];

%o (PARI) a(n)=6^n-6*n \\ _Charles R Greathouse IV_, Jul 06 2017

%Y Cf. A005803, A107583, A107584, A107585.

%K nonn,easy

%O 0,3

%A _Vincenzo Librandi_, Oct 26 2011