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 A161549 #41 Oct 27 2024 16:08:24
%S A161549 1,17,37,61,89,121,157,197,241,289,341,397,457,521,589,661,737,817,
%T A161549 901,989,1081,1177,1277,1381,1489,1601,1717,1837,1961,2089,2221,2357,
%U A161549 2497,2641,2789,2941,3097,3257,3421,3589,3761,3937,4117,4301,4489,4681,4877,5077
%N A161549 a(n) = 2*n^2 + 14*n + 1.
%C A161549 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 A161549 Pierre Gayet, <a href="/A161549/b161549.txt">Table of n, a(n) for n = 0..9999</a>
%H A161549 Pierre Gayet, <a href="/A162316/a162316.gif">Note et Compte rendu</a> (gif version).
%H A161549 Pierre Gayet, <a href="/A162316/a162316.pdf">Note et Compte Rendu</a> (pdf version).
%H A161549 Pierre Gayet, <a href="/A162316/a162316_1.txt">98 séquences générées ... par la formule générale indiquée</a>.
%H A161549 Claude Monet, <a href="https://web.archive.org/web/20060428022333/http://lycees.ac-rouen.fr/bruyeres/jardin/Nymphea.html">Nymphéas</a>.
%H A161549 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A161549 a(n) = a(n-1) + 4*n + 12 (with a(0)=1). - _Vincenzo Librandi_, Nov 30 2010
%F A161549 G.f.: (1 + 14*x - 11*x^2)/(1-x)^3. - _Vincenzo Librandi_, Nov 08 2014
%F A161549 From _Elmo R. Oliveira_, Oct 25 2024: (Start)
%F A161549 E.g.f.: (1 + 16*x + 2*x^2)*exp(x).
%F A161549 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)
%t A161549 lst={}; Do[a=2*n^2+14*n+1; AppendTo[lst, a], {n, 0, 5!}]; lst (* _Vladimir Joseph Stephan Orlovsky_, Jun 13 2009 *)
%t A161549 CoefficientList[Series[(1 + 14 x - 11 x^2) / (1 - x)^3, {x, 0, 50}], x] (* _Vincenzo Librandi_, Nov 08 2014 *)
%t A161549 Table[2n^2+14n+1,{n,0,50}] (* or *) LinearRecurrence[{3,-3,1},{1,17,37},50] (* _Harvey P. Dale_, Jul 14 2018 *)
%o A161549 (Magma) [ 2*n^2+14*n+1: n in [0..50] ];
%o A161549 (PARI) Vec((1+14*x-11*x^2)/(1-x)^3 + O(x^100)) \\ _Colin Barker_, Nov 08 2014
%Y A161549 Cf. A161532, A161587, A161617, A161935, A162316.
%K A161549 easy,nonn
%O A161549 0,2
%A A161549 _Pierre Gayet_, Jun 13 2009
%E A161549 More terms from _Vladimir Joseph Stephan Orlovsky_, Jun 13 2009