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 A119032 #28 Dec 02 2024 09:45:03
%S A119032 0,9,170,3059,54900,985149,17677790,317215079,5692193640,102142270449,
%T A119032 1832868674450,32889493869659,590178020979420,10590314883759909,
%U A119032 190035489886698950,3410048503076821199,61190837565496082640,1098025027675852666329,19703259660599851911290
%N A119032 a(n+2) = 18*a(n+1) - a(n) + 8.
%C A119032 Arises in calculating A107075. A053606 follows the same recurrence.
%H A119032 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (19,-19,1).
%F A119032 a(n+1) = 9*a(n+1) + 4 + (80*a(n)^2+80*a(n)+25)^(1/2).
%F A119032 G.f.: (9*x-x^2)/((1-x)*(1-18*x+x^2)).
%F A119032 a(n) = ((sqrt(5)+2)/8)*(9+4*sqrt(5))^(n-1) + ((-sqrt(5)+2)/8)*(9-4*sqrt(5))^(n-1) - 1/2. - _Richard Choulet_, Nov 26 2008
%F A119032 a(n) = (Lucas(6*n-3)-4)/8, where Lucas(n) = A000032(n). - _Gary Detlefs_, Dec 07 2010
%F A119032 Product_{n>=2} (1 + 1/a(n)) = sqrt(5)/2 (= 10 * A020837). - _Amiram Eldar_, Dec 02 2024
%t A119032 LinearRecurrence[{19, -19, 1}, {0, 9, 170}, 20] (* _Amiram Eldar_, Dec 02 2024 *)
%Y A119032 Cf. A000032, A020837, A053606, A107075.
%K A119032 nonn,easy
%O A119032 1,2
%A A119032 _Richard Choulet_, Aug 30 2007, Oct 09 2007