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A161617 a(n) = 8*n^2 + 20*n + 1.

%I A161617 #19 Oct 22 2024 20:16:16
%S A161617 1,29,73,133,209,301,409,533,673,829,1001,1189,1393,1613,1849,2101,
%T A161617 2369,2653,2953,3269,3601,3949,4313,4693,5089,5501,5929,6373,6833,
%U A161617 7309,7801,8309,8833,9373,9929,10501,11089,11693,12313,12949,13601,14269,14953,15653,16369
%N A161617 a(n) = 8*n^2 + 20*n + 1.
%C A161617 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 P. Gayet)
%H A161617 Pierre Gayet, <a href="/A161617/b161617.txt">Table of n, a(n) for n = 0..9999</a>.
%H A161617 Pierre Gayet, <a href="/A162316/a162316.gif">Note et Compte rendu</a> (gif version).
%H A161617 Pierre Gayet, <a href="/A162316/a162316.pdf">Note et Compte Rendu</a> (pdf version).
%H A161617 Pierre Gayet, <a href="/A162316/a162316_1.txt">98 séquences générées ... par la formule générale indiquée</a>.
%H A161617 Claude Monet, <a href="http://lycees.ac-rouen.fr/bruyeres/jardin/Nymphea.html">Nymphéas</a>.
%H A161617 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A161617 a(n) = a(n-1) + 16*n + 12 (with a(0)=1). - _Vincenzo Librandi_, Nov 30 2010
%F A161617 From _Elmo R. Oliveira_, Oct 22 2024: (Start)
%F A161617 G.f.: (1 + 26*x - 11*x^2)/(1 - x)^3.
%F A161617 E.g.f.: (1 + 28*x + 8*x^2)*exp(x).
%F A161617 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)
%o A161617 (Magma) [ 8*n^2+20*n+1: n in [0..50] ];
%o A161617 (PARI) a(n)=8*n^2+20*n+1 \\ _Charles R Greathouse IV_, Jun 17 2017
%Y A161617 Cf. A161532, A161549, A161587, A161935, A162316.
%K A161617 easy,nonn
%O A161617 0,2
%A A161617 _Pierre Gayet_, Jun 14 2009