A014882 - OEIS

%I #34 Feb 10 2024 11:34:44

%S 1,14,171,2056,24677,296130,3553567,42642812,511713753,6140565046,

%T 73686780563,884241366768,10610896401229,127330756814762,

%U 1527969081777159,18335628981325924,220027547775911105,2640330573310933278,31683966879731199355

%N a(1) = 1, a(n) = 12*a(n-1) + n.

%H Vincenzo Librandi, <a href="/A014882/b014882.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 (14,-25,12).

%F a(n) = 14*a(n-1)-25*a(n-2)+12*a(n-3), with a(1)=1, a(2)=14, a(3)=171. - _Vincenzo Librandi_, Oct 20 2012

%F G.f.: x/((1-12*x)*(1-x)^2). - _Jinyuan Wang_, Mar 11 2020

%p a:=n->sum((12^(n-j)-1^(n-j))/11,j=0..n): seq(a(n), n=1..17); # _Zerinvary Lajos_, Jan 12 2007

%p a:= n-> (Matrix([[1,0,1],[1,1,1],[0,0,12]])^n)[2,3]:

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

%t LinearRecurrence[{14, -25, 12}, {1, 14, 171}, 201] (* _Vincenzo Librandi_, Oct 20 2012 *)

%o (Magma) I:=[1, 14, 171]; [n le 3 select I[n] else 14*Self(n-1) - 25*Self(n-2)+ 12*Self(n-3): n in [1..20]]; // _Vincenzo Librandi_, Oct 20 2012

%K nonn

%O 1,2

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