OFFSET
0,2
COMMENTS
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]
Numbers of the form 2*n^2 - 7. - Boris Putievskiy, Feb 04 2013
LINKS
Pierre Gayet, Table of n, a(n) for n = 0..10000
Pierre Gayet, Note et Compte rendu (gif version).
Pierre Gayet, Note et Compte Rendu (pdf version).
Pierre Gayet, 98 séquences générées ... par la formule générale indiquée.
Claude Monet, Nymphéas.
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
a(n) = a(n-1) + 4*n + 6 (with a(0)=1). - Vincenzo Librandi, Nov 30 2010
G.f.: (1 + 8*x - 5*x^2)/(1 - x)^3. - Vincenzo Librandi, Feb 07 2013
From Elmo R. Oliveira, Oct 27 2024: (Start)
E.g.f.: (1 + 10*x + 2*x^2)*exp(x).
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)
MATHEMATICA
Table[2*n^2+8*n+1, {n, 0, 100}] (* Vladimir Joseph Stephan Orlovsky, Jun 13 2009 *)
CoefficientList[Series[(1 + 8*x - 5*x^2)/(1-x)^3, {x, 0, 60}], x] (* Vincenzo Librandi, Feb 07 2013 *)
PROG
(Magma) [ 2*n^2+8*n+1: n in [0..50] ];
(PARI) a(n)=2*n^2+8*n+1 \\ Charles R Greathouse IV, Jun 17 2017
CROSSREFS
KEYWORD
easy,nonn,changed
AUTHOR
Pierre Gayet, Jun 13 2009
EXTENSIONS
More terms from Vladimir Joseph Stephan Orlovsky, Jun 13 2009
STATUS
approved