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 A162316 #59 Oct 27 2024 10:46:37
%S A162316 1,26,61,106,161,226,301,386,481,586,701,826,961,1106,1261,1426,1601,
%T A162316 1786,1981,2186,2401,2626,2861,3106,3361,3626,3901,4186,4481,4786,
%U A162316 5101,5426,5761,6106,6461,6826,7201,7586,7981,8386,8801,9226,9661,10106,10561,11026
%N A162316 a(n) = 5*n^2 + 20*n + 1.
%C A162316 The defining formula can be regarded as an approximation and simplification of the expansion / propagation of native hydrophytes on the surface of stagnant waters in orthogonal directions; absence of competition / concurrence and of retrogression is assumed, mortality is taken into account. - [Translation of a comment in French sent by _Pierre Gayet_]
%H A162316 Pierre Gayet, <a href="/A162316/b162316.txt">Table of n, a(n) for n = 0..9999</a>
%H A162316 Pierre Gayet, <a href="/A162316/a162316.gif">Note et Compte rendu</a> (gif version).
%H A162316 Pierre Gayet, <a href="/A162316/a162316.pdf">Note et Compte Rendu</a> (pdf version).
%H A162316 Pierre Gayet, <a href="/A162316/a162316_1.txt">98 séquences générées ... par la formule générale indiquée</a>.
%H A162316 Claude Monet, <a href="https://web.archive.org/web/20060428022333/http://lycees.ac-rouen.fr/bruyeres/jardin/Nymphea.html">Nymphéas</a>.
%H A162316 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A162316 a(n) = a(n-1) + 10*n + 15 (with a(0)=1). - _Vincenzo Librandi_, Dec 02 2010
%F A162316 G.f.: (14*x^2 - 23*x - 1)/(x - 1)^3. - _Harvey P. Dale_, May 07 2023
%F A162316 From _Elmo R. Oliveira_, Oct 25 2024: (Start)
%F A162316 E.g.f.: (5*x^2 + 25*x + 1)*exp(x).
%F A162316 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)
%t A162316 lst={}; Do[a=5*n^2+20*n+1; AppendTo[lst, a], {n, 0, 5!}]; lst
%t A162316 Table[5n^2+20n+1,{n,0,40}] (* or *) LinearRecurrence[{3,-3,1},{1,26,61},40] (* or *) CoefficientList[Series[(14x^2-23x-1)/(x-1)^3,{x,0,40}],x] (* _Harvey P. Dale_, May 07 2023 *)
%o A162316 (Magma) [ 5*n^2+20*n+1: n in [0..50] ];
%o A162316 (PARI) a(n)=5*n^2+20*n+1 \\ _Charles R Greathouse IV_, Jun 17 2017
%Y A162316 Cf. A161532, A161549, A161587, A161617, A161935.
%K A162316 easy,nonn
%O A162316 0,2
%A A162316 _Pierre Gayet_, Jul 01 2009