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) + 26*n - 3 (with a(0)=1). - Vincenzo Librandi, Nov 30 2010
From Bruno Berselli, Dec 12 2011: (Start)
G.f.: (1 + 21*x + 4*x^2)/(1-x)^3.
a(n-1) = A202141(n) - 1 with a(-1)=4. (End)
E.g.f.: exp(x)*(1 + 23*x + 13*x^2). - Stefano Spezia, Oct 21 2024
MATHEMATICA
Table[13n^2+10n+1, {n, 0, 40}] (* or *) LinearRecurrence[{3, -3, 1}, {1, 24, 73}, 40] (* Harvey P. Dale, Nov 06 2014 *)
PROG
(Magma) [ 13*n^2+10*n+1: n in [0..50] ];
(PARI) a(n)=13*n^2+10*n+1 \\ Charles R Greathouse IV, Oct 07 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Pierre Gayet, Jun 14 2009
STATUS
approved