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 A157262 #37 Sep 08 2022 08:45:41
%S A157262 2,55,180,377,646,987,1400,1885,2442,3071,3772,4545,5390,6307,7296,
%T A157262 8357,9490,10695,11972,13321,14742,16235,17800,19437,21146,22927,
%U A157262 24780,26705,28702,30771,32912,35125,37410,39767,42196,44697,47270
%N A157262 a(n) = 36*n^2 - 55*n + 21.
%C A157262 The identity (10368*n^2 - 15840*n + 6049)^2 - (36*n^2 - 55*n + 21)*(1728*n - 1320)^2 = 1 can be written as A157264(n)^2 - a(n)*A157263(n)^2 = 1. - _Vincenzo Librandi_, Jan 27 2012
%C A157262 The continued fraction expansion of sqrt(a(n)) is [6n-5; {2, 2, 2, 12n-10}]. For n=1, this collapses to [1; {2}]. - _Magus K. Chu_, Sep 05 2022
%H A157262 Vincenzo Librandi, <a href="/A157262/b157262.txt">Table of n, a(n) for n = 1..10000</a>
%H A157262 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A157262 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - _Vincenzo Librandi_, Jan 27 2012
%F A157262 G.f.: x*(-2-49*x-21*x^2)/(x-1)^3. - _Vincenzo Librandi_, Jan 27 2012
%F A157262 a(n) = A016813(n-1)*A017185(n-1). - _Bruno Berselli_, Jan 27 2012
%F A157262 E.g.f.: (36*x^2 - 19*x + 21)*exp(x) - 21. - _G. C. Greubel_, Feb 04 2018
%t A157262 LinearRecurrence[{3,-3,1},{2,55,180},40] (* _Vincenzo Librandi_, Jan 27 2012 *)
%t A157262 Table[36*n^2-55*n+21, {n,1,30}] (* _G. C. Greubel_, Feb 04 2018 *)
%o A157262 (PARI) a(n)=36*n^2-55*n+21 \\ _Charles R Greathouse IV_, Dec 28 2011
%o A157262 (Magma) I:=[2, 55, 180]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]]; // _Vincenzo Librandi_, Jan 27 2012
%Y A157262 Cf. A157263, A157264.
%K A157262 nonn,easy
%O A157262 1,1
%A A157262 _Vincenzo Librandi_, Feb 26 2009