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]
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) + 10*n + 15 (with a(0)=1). - Vincenzo Librandi, Dec 02 2010
G.f.: (14*x^2 - 23*x - 1)/(x - 1)^3. - Harvey P. Dale, May 07 2023
From Elmo R. Oliveira, Oct 25 2024: (Start)
E.g.f.: (5*x^2 + 25*x + 1)*exp(x).
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)
MATHEMATICA
lst={}; Do[a=5*n^2+20*n+1; AppendTo[lst, a], {n, 0, 5!}]; lst
Table[5n^2+20n+1, {n, 0, 40}] (* or *) LinearRecurrence[{3, -3, 1}, {1, 26, 61}, 40] (* or *) CoefficientList[Series[(14x^2-23x-1)/(x-1)^3, {x, 0, 40}], x] (* Harvey P. Dale, May 07 2023 *)
PROG
(Magma) [ 5*n^2+20*n+1: n in [0..50] ];
(PARI) a(n)=5*n^2+20*n+1 \\ Charles R Greathouse IV, Jun 17 2017
CROSSREFS
KEYWORD
easy,nonn,changed
AUTHOR
Pierre Gayet, Jul 01 2009
STATUS
approved