login
A161617
a(n) = 8*n^2 + 20*n + 1.
6
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
0,2
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 P. Gayet)
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)
PROG
(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
CROSSREFS
KEYWORD
easy,nonn,changed
AUTHOR
Pierre Gayet, Jun 14 2009
STATUS
approved