A199021 - OEIS

%I #20 Apr 02 2025 20:12:20

%S 2,27,302,3327,36602,402627,4428902,48717927,535897202,5894869227,

%T 64843561502,713279176527,7846070941802,86306780359827,

%U 949374583958102,10443120423539127,114874324658930402,1263617571248234427,13899793283730578702,152897726121036365727,1681874987331400023002

%N a(n) = (5*11^n - 1)/2.

%H Vincenzo Librandi, <a href="/A199021/b199021.txt">Table of n, a(n) for n = 0..900</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (12,-11).

%F a(n) = 11*a(n-1) + 5.

%F a(n) = 12*a(n-1) - 11*a(n-2), n > 1.

%F G.f.: (2 + 3*x)/(1 - 12*x + 11*x^2). - _Vincenzo Librandi_, Jan 04 2013

%F From _Elmo R. Oliveira_, Apr 02 2025: (Start)

%F E.g.f.: exp(x)*(5*exp(10*x) - 1)/2.

%F a(n) = A199022(n)/2. (End)

%t CoefficientList[Series[(2 + 3*x)/(1 - 12*x + 11*x^2), {x, 0, 30}], x] (* _Vincenzo Librandi_, Jan 04 2013 *)

%t LinearRecurrence[{12,-11},{2,27},20] (* _Harvey P. Dale_, Aug 13 2018 *)

%o (Magma) [(5*11^n-1)/2 : n in [0..20]];

%Y Cf. A199022.

%K nonn,easy

%O 0,1

%A _Vincenzo Librandi_, Nov 02 2011