OFFSET
0,3
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]
These are also the star 14-gonal numbers: a(n) = A051866(n) + 14*A000217(n-1). Luciano Ancora, Apr 04 2015
LINKS
Daniel Mondot, Table of n, a(n) for n = 0..1000
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+1) = a(n) + 26*n + 1. - Vincenzo Librandi, Nov 30 2010
Product_{n>=2} (1 - 1/a(n)) = 13/14. - Amiram Eldar, Jan 22 2021
E.g.f.: exp(x)*(x + 13*x^2). - Nikolaos Pantelidis, Feb 05 2023
EXAMPLE
G.f. = x + 28*x^2 + 81*x^3 + 160*x^4 + 265*x^5 + 396*x^6 + 553*x^7 + ...
MATHEMATICA
lst={}; Do[a=13*n^2+14*n+1; AppendTo[lst, a], {n, 0, 5!}]; lst
Table[n*(13*n - 12), {n, 0, 100}] (* Robert Price, Oct 11 2018 *)
PROG
(Magma) [ (n+1)*(13*n+1): n in[0..50] ];
(PARI) {a(n) = n*(13*n - 12)}; /* Michael Somos, Dec 07 2016 */
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Pierre Gayet, Jun 22 2009
EXTENSIONS
Edited by N. J. A. Sloane, Dec 07 2016 at the suggestion of Daniel Sterman.
Definition simplified by Omar E. Pol, Aug 10 2018
STATUS
approved