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 P. Gayet)
LINKS
Pierre Gayet, Table of n, a(n) for n = 0..9999.
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) + 16*n + 12 (with a(0)=1). - Vincenzo Librandi, Nov 30 2010
From Elmo R. Oliveira, Oct 22 2024: (Start)
G.f.: (1 + 26*x - 11*x^2)/(1 - x)^3.
E.g.f.: (1 + 28*x + 8*x^2)*exp(x).
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)
PROG
(Magma) [ 8*n^2+20*n+1: n in [0..50] ];
(PARI) a(n)=8*n^2+20*n+1 \\ Charles R Greathouse IV, Jun 17 2017
CROSSREFS
KEYWORD
easy,nonn,changed
AUTHOR
Pierre Gayet, Jun 14 2009
STATUS
approved