This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A014882 #38 Mar 31 2025 13:38:35
%S A014882 1,14,171,2056,24677,296130,3553567,42642812,511713753,6140565046,
%T A014882 73686780563,884241366768,10610896401229,127330756814762,
%U A014882 1527969081777159,18335628981325924,220027547775911105,2640330573310933278,31683966879731199355,380207602556774392280
%N A014882 a(1) = 1, a(n) = 12*a(n-1) + n.
%H A014882 Vincenzo Librandi, <a href="/A014882/b014882.txt">Table of n, a(n) for n = 1..200</a>
%H A014882 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (14,-25,12).
%F A014882 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 A014882 G.f.: x/((1-12*x)*(1-x)^2). - _Jinyuan Wang_, Mar 11 2020
%F A014882 From _Elmo R. Oliveira_, Mar 31 2025: (Start)
%F A014882 E.g.f.: exp(x)*(12*exp(11*x) - 11*x - 12)/121.
%F A014882 a(n) = (12^(n+1) - 11*n - 12)/121. (End)
%p A014882 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 A014882 a:= n-> (Matrix([[1,0,1],[1,1,1],[0,0,12]])^n)[2,3]:
%p A014882 seq(a(n), n=1..17); # _Alois P. Heinz_, Aug 06 2008
%t A014882 LinearRecurrence[{14, -25, 12}, {1, 14, 171}, 201] (* _Vincenzo Librandi_, Oct 20 2012 *)
%o A014882 (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
%Y A014882 Row n=12 of A126885.
%K A014882 nonn,easy
%O A014882 1,2
%A A014882 _N. J. A. Sloane_, _Olivier Gérard_