# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a161617 Showing 1-1 of 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, Table of n, a(n) for n = 0..9999. %H A161617 Pierre Gayet, Note et Compte rendu (gif version). %H A161617 Pierre Gayet, Note et Compte Rendu (pdf version). %H A161617 Pierre Gayet, 98 séquences générées ... par la formule générale indiquée. %H A161617 Claude Monet, Nymphéas. %H A161617 Index entries for linear recurrences with constant coefficients, 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 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE