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A161532
a(n) = 2*n^2 + 8*n + 1.
13
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, 4795, 4993
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
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
From Elmo R. Oliveira, Oct 27 2024: (Start)
E.g.f.: (1 + 10*x + 2*x^2)*exp(x).
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)
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
KEYWORD
easy,nonn,changed
AUTHOR
Pierre Gayet, Jun 13 2009
EXTENSIONS
More terms from Vladimir Joseph Stephan Orlovsky, Jun 13 2009
STATUS
approved