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 A154254 #51 Oct 19 2024 13:44:53
%S A154254 2,3,22,59,114,187,278,387,514,659,822,1003,1202,1419,1654,1907,2178,
%T A154254 2467,2774,3099,3442,3803,4182,4579,4994,5427,5878,6347,6834,7339,
%U A154254 7862,8403,8962,9539,10134,10747,11378,12027,12694,13379,14082,14803,15542,16299,17074,17867
%N A154254 a(n) = 9*n^2 - 8*n + 2.
%C A154254 The identity (81*n^2 + 90*n + 26)^2 - (9*n^2 + 10*n + 3)*(27*n + 15)^2 = 1 can be written as A154277(n+1)^2 - a(n+1)*A154267(n)^2 = 1. - _Vincenzo Librandi_, Feb 03 2012
%C A154254 For n >= 1, the continued fraction expansion of sqrt(a(n)) is [3n-2; {1, 2, 3n-2, 2, 1, 6n-4}]. For n=1, this collapses to [1; {1, 2}]. - _Magus K. Chu_, Sep 09 2022
%H A154254 Vincenzo Librandi, <a href="/A154254/b154254.txt">Table of n, a(n) for n = 0..10000</a>
%H A154254 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A154254 From _Vincenzo Librandi_, Jan 30 2012: (Start)
%F A154254 G.f.: (2 - 3*x + 19*x^2)/(1-x)^3.
%F A154254 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). (End)
%F A154254 E.g.f.: exp(x)*(2 + x + 9*x^2). - _Elmo R. Oliveira_, Oct 19 2024
%t A154254 LinearRecurrence[{3, -3, 1}, {2, 3, 22}, 50] (* _Vincenzo Librandi_, Jan 30 2012 *)
%o A154254 (PARI) a(n)=9*n^2-8*n+2 \\ _Charles R Greathouse IV_, Dec 27 2011
%o A154254 (Magma) I:=[2, 3, 22]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]]; // _Vincenzo Librandi_, Jan 29 2012
%Y A154254 Cf. A154267, A154277.
%K A154254 nonn,easy
%O A154254 0,1
%A A154254 _Vincenzo Librandi_, Jan 05 2009
%E A154254 7662 replaced by 7862 by _R. J. Mathar_, Jan 07 2009
%E A154254 Edited by _Charles R Greathouse IV_, Jul 25 2010