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) + 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)
MATHEMATICA
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 *)
PROG
(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
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Pierre Gayet, Jun 13 2009
EXTENSIONS
More terms from Vladimir Joseph Stephan Orlovsky, Jun 13 2009
STATUS
approved