A161587 a(n) = 13n^2 + 10n + 1.

1, 24, 73, 148, 249, 376, 529, 708, 913, 1144, 1401, 1684, 1993, 2328, 2689, 3076, 3489, 3928, 4393, 4884, 5401, 5944, 6513, 7108, 7729, 8376, 9049, 9748, 10473, 11224, 12001, 12804, 13633, 14488, 15369, 16276, 17209, 18168, 19153, 20164

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)

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

Cf. A161532, A161549, A161617, A161935, A162316.

Sequence in context: A043406 A044162 A044543 * A042130 A042132 A042134

Adjacent sequences: A161584 A161585 A161586 * A161588 A161589 A161590

Keyword

nonn,easy

Author

Pierre Gayet, Jun 14 2009

Status

approved