A161587 a(n) = 13*n^2 + 10*n + 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

Author

Pierre Gayet, Jun 14 2009

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A161532, A161549, A161617, A161935, A162316, A202141.

Programs

Magma

[ 13*n^2+10*n+1: n in [0..50] ];

Mathematica

Table[13n^2+10n+1,{n,0,40}] (* or *) LinearRecurrence[{3,-3,1},{1,24,73},40] (* Harvey P. Dale, Nov 06 2014 *)

PARI

a(n)=13*n^2+10*n+1 \\ Charles R Greathouse IV, Oct 07 2015

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