A161532 a(n) = 2n^2 + 8n + 1.

1, 11, 25, 43, 65, 91, 121, 155, 193, 235, 281, 331, 385, 443, 505, 571, 641, 715, 793, 875, 961, 1051, 1145, 1243, 1345, 1451, 1561, 1675, 1793, 1915, 2041, 2171, 2305, 2443, 2585, 2731, 2881, 3035, 3193, 3355, 3521, 3691, 3865, 4043, 4225, 4411, 4601

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]

Numbers of the form 2*n^2 - 7. - Boris Putievskiy, Feb 04 2013

Links

Pierre Gayet, Table of n, a(n) for n = 0..10000

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) + 4*n + 6 (with a(0)=1). - Vincenzo Librandi, Nov 30 2010

G.f.: (1 + 8*x - 5*x^2)/(1 - x)^3. - Vincenzo Librandi, Feb 07 2013

Mathematica

Table[2*n^2+8*n+1, {n, 0, 100}] (* Vladimir Joseph Stephan Orlovsky, Jun 13 2009 *)
CoefficientList[Series[(1 + 8*x - 5*x^2)/(1-x)^3, {x, 0, 60}], x] (* Vincenzo Librandi, Feb 07 2013 *)

Prog

(Magma) [ 2*n^2+8*n+1: n in [0..50] ];
(PARI) a(n)=2*n^2+8*n+1 \\ Charles R Greathouse IV, Jun 17 2017

Crossrefs

Cf. A161549, A161587, A161617, A161935, A162316.

Sequence in context: A301635 A031025 A140675 * A328560 A118648 A262105

Adjacent sequences: A161529 A161530 A161531 * A161533 A161534 A161535

Keyword

easy,nonn

Author

Pierre Gayet, Jun 13 2009

Extensions

More terms from Vladimir Joseph Stephan Orlovsky, Jun 13 2009

Status

approved