0,2

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]

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).

a(n) = a(n-1) + 4*n + 12 (with a(0)=1). - Vincenzo Librandi, Nov 30 2010

G.f.: (1 + 14*x - 11*x^2)/(1-x)^3. - Vincenzo Librandi, Nov 08 2014

From Elmo R. Oliveira, Oct 25 2024: (Start)

E.g.f.: (1 + 16*x + 2*x^2)*exp(x).

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)

lst={}; Do[a=2*n^2+14*n+1; AppendTo[lst, a], {n, 0, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Jun 13 2009 *)

CoefficientList[Series[(1 + 14 x - 11 x^2) / (1 - x)^3, {x, 0, 50}], x] (* Vincenzo Librandi, Nov 08 2014 *)

Table[2n^2+14n+1, {n, 0, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {1, 17, 37}, 50] (* Harvey P. Dale, Jul 14 2018 *)

(Magma) [ 2*n^2+14*n+1: n in [0..50] ];

(PARI) Vec((1+14*x-11*x^2)/(1-x)^3 + O(x^100)) \\ Colin Barker, Nov 08 2014

Cf. A161532, A161587, A161617, A161935, A162316.

Sequence in context: A341937 A225077 A146328 * A269788 A146348 A050952

Adjacent sequences: A161546 A161547 A161548 * A161550 A161551 A161552

easy,nonn

Pierre Gayet, Jun 13 2009

More terms from Vladimir Joseph Stephan Orlovsky, Jun 13 2009

approved