A161617 a(n) = 8*n^2 + 20*n + 1.

1, 29, 73, 133, 209, 301, 409, 533, 673, 829, 1001, 1189, 1393, 1613, 1849, 2101, 2369, 2653, 2953, 3269, 3601, 3949, 4313, 4693, 5089, 5501, 5929, 6373, 6833, 7309, 7801, 8309, 8833, 9373, 9929, 10501, 11089, 11693, 12313, 12949, 13601, 14269, 14953, 15653, 16369

Offset: 0

Author

Pierre Gayet, Jun 14 2009

Keywords

• easy
• nonn

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 P. 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, A161587, A161935, A162316.

Programs

Magma

[ 8*n^2+20*n+1: n in [0..50] ];

PARI

a(n)=8*n^2+20*n+1 \\ Charles R Greathouse IV, Jun 17 2017

Formula

a(n) = a(n-1) + 16*n + 12 (with a(0)=1). - Vincenzo Librandi, Nov 30 2010

From Elmo R. Oliveira, Oct 22 2024: (Start)

G.f.: (1 + 26*x - 11*x^2)/(1 - x)^3.

E.g.f.: (1 + 28*x + 8*x^2)*exp(x).

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)