A014881 - OEIS

%I #37 Feb 10 2024 11:34:39

%S 1,13,146,1610,17715,194871,2143588,23579476,259374245,2853116705,

%T 31384283766,345227121438,3797498335831,41772481694155,

%U 459497298635720,5054470284992936,55599173134922313,611590904484145461,6727499949325600090

%N a(1)=1, a(n) = 11*a(n-1)+n.

%H Vincenzo Librandi, <a href="/A014881/b014881.txt">Table of n, a(n) for n = 1..200</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (13,-23,11).

%F a(n) = 13*a(n-1)-23*a(n-2)+11*a(n-3), with a(1)=1, a(2)=13, a(3)=146. - _Vincenzo Librandi_, Oct 20 2012

%F G.f.: x/((1-11*x)*(1-x)^2). - _Jinyuan Wang_, Mar 11 2020

%p a:= n-> (Matrix([[1,0,1],[1,1,1],[0,0,11]])^n)[2,3]:

%p seq(a(n), n=1..17);  # _Alois P. Heinz_, Aug 06 2008

%t LinearRecurrence[{13, -23, 11}, {1, 13, 146}, 20] (* _Vincenzo Librandi_, Oct 20 2012 *)

%o (Magma) I:=[1, 13, 146]; [n le 3 select I[n] else 13*Self(n-1) - 23*Self(n-2)+ 11*Self(n-3): n in [1..20]]; // _Vincenzo Librandi_, Oct 20 2012

%K nonn

%O 1,2

%A _N. J. A. Sloane_, _Olivier Gérard_