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)
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
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
AUTHOR
Pierre Gayet, Jun 13 2009
EXTENSIONS
More terms from Vladimir Joseph Stephan Orlovsky, Jun 13 2009
STATUS
approved