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 A161532 #45 Oct 27 2024 14:29:44
%S A161532 1,11,25,43,65,91,121,155,193,235,281,331,385,443,505,571,641,715,793,
%T A161532 875,961,1051,1145,1243,1345,1451,1561,1675,1793,1915,2041,2171,2305,
%U A161532 2443,2585,2731,2881,3035,3193,3355,3521,3691,3865,4043,4225,4411,4601,4795,4993
%N A161532 a(n) = 2*n^2 + 8*n + 1.
%C A161532 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_]
%C A161532 Numbers of the form 2*n^2 - 7. - _Boris Putievskiy_, Feb 04 2013
%H A161532 Pierre Gayet, <a href="/A161532/b161532.txt">Table of n, a(n) for n = 0..10000</a>
%H A161532 Pierre Gayet, <a href="/A162316/a162316.gif">Note et Compte rendu</a> (gif version).
%H A161532 Pierre Gayet, <a href="/A162316/a162316.pdf">Note et Compte Rendu</a> (pdf version).
%H A161532 Pierre Gayet, <a href="/A162316/a162316_1.txt">98 séquences générées ... par la formule générale indiquée</a>.
%H A161532 Claude Monet, <a href="https://web.archive.org/web/20060428022333/http://lycees.ac-rouen.fr/bruyeres/jardin/Nymphea.html">Nymphéas</a>.
%H A161532 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A161532 a(n) = a(n-1) + 4*n + 6 (with a(0)=1). - _Vincenzo Librandi_, Nov 30 2010
%F A161532 G.f.: (1 + 8*x - 5*x^2)/(1 - x)^3. - _Vincenzo Librandi_, Feb 07 2013
%F A161532 From _Elmo R. Oliveira_, Oct 27 2024: (Start)
%F A161532 E.g.f.: (1 + 10*x + 2*x^2)*exp(x).
%F A161532 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)
%t A161532 Table[2*n^2+8*n+1, {n,0,100}] (* _Vladimir Joseph Stephan Orlovsky_, Jun 13 2009 *)
%t A161532 CoefficientList[Series[(1 + 8*x - 5*x^2)/(1-x)^3, {x, 0, 60}], x] (* _Vincenzo Librandi_, Feb 07 2013 *)
%o A161532 (Magma) [ 2*n^2+8*n+1: n in [0..50] ];
%o A161532 (PARI) a(n)=2*n^2+8*n+1 \\ _Charles R Greathouse IV_, Jun 17 2017
%Y A161532 Cf. A161549, A161587, A161617, A161935, A162316.
%K A161532 easy,nonn
%O A161532 0,2
%A A161532 _Pierre Gayet_, Jun 13 2009
%E A161532 More terms from _Vladimir Joseph Stephan Orlovsky_, Jun 13 2009