A162316 a(n) = 5n^2 + 20n + 1.

1, 26, 61, 106, 161, 226, 301, 386, 481, 586, 701, 826, 961, 1106, 1261, 1426, 1601, 1786, 1981, 2186, 2401, 2626, 2861, 3106, 3361, 3626, 3901, 4186, 4481, 4786, 5101, 5426, 5761, 6106, 6461, 6826

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

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

Cf. A161532, A161549, A161587, A161617, A161935.

Sequence in context: A277976 A291105 A267294 * A173085 A044128 A044509

Adjacent sequences: A162313 A162314 A162315 * A162317 A162318 A162319

Keyword

easy,nonn

Author

Pierre Gayet, Jul 01 2009

Status

approved