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 A156735 #28 Jan 30 2024 19:29:42
%S A156735 9801,114243,332929,665859,1113033,1674451,2350113,3140019,4044169,
%T A156735 5062563,6195201,7442083,8803209,10278579,11868193,13572051,15390153,
%U A156735 17322499,19369089,21529923,23805001,26194323,28697889,31315699
%N A156735 a(n) = 57122*n^2 + 47320*n + 9801.
%C A156735 The identity (57122*n^2 +47320*n +9801)^2 - (169*n^2 +140*n +29)*(4394*n +1820)^2 = 1 can be written as a(n)^2 - A156640(n)*A156636(n)^2 = 1.
%H A156735 Vincenzo Librandi, <a href="/A156735/b156735.txt">Table of n, a(n) for n = 0..10000</a>
%H A156735 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A156735 a(n) = 3*a(n-1) -3*a(n-2) +a(n-3) for n>2.
%F A156735 G.f.: (9801 + 84840*x + 19603*x^2)/(1 - x)^3. - _Vincenzo Librandi_, May 03 2014
%F A156735 E.g.f.: (9801 +104442*x +57122*x^2)*exp(x). - _G. C. Greubel_, Feb 28 2021
%p A156735 A156735:= n-> 57122*n^2 + 47320*n + 9801; seq(A156735(n), n=0..50); # _G. C. Greubel_, Feb 28 2021
%t A156735 LinearRecurrence[{3,-3,1},{9801,114243,332929},50]
%t A156735 CoefficientList[Series[(9801 +84840x +19603x^2)/(1-x)^3, {x, 0, 60}], x] (* _Vincenzo Librandi_, May 03 2014 *)
%t A156735 Table[57122n^2+47320n+9801,{n,0,30}] (* _Harvey P. Dale_, Jan 30 2024 *)
%o A156735 (Magma) I:=[9801, 114243, 332929]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]];
%o A156735 (PARI) a(n)= 57122*n^2+47320*n+9801 \\ _Charles R Greathouse IV_, Dec 23 2011
%o A156735 (Sage) [57122*n^2 + 47320*n + 9801 for n in (0..50)] # _G. C. Greubel_, Feb 28 2021
%Y A156735 Cf. A156636, A156640, A156718.
%K A156735 nonn,easy
%O A156735 0,1
%A A156735 _Vincenzo Librandi_, Feb 15 2009
%E A156735 Edited by _Charles R Greathouse IV_, Jul 25 2010