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A162316
a(n) = 5*n^2 + 20*n + 1.
6
1, 26, 61, 106, 161, 226, 301, 386, 481, 586, 701, 826, 961, 1106, 1261, 1426, 1601, 1786, 1981, 2186, 2401, 2626, 2861, 3106, 3361, 3626, 3901, 4186, 4481, 4786, 5101, 5426, 5761, 6106, 6461, 6826, 7201, 7586, 7981, 8386, 8801, 9226, 9661, 10106, 10561, 11026
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]
FORMULA
a(n) = a(n-1) + 10*n + 15 (with a(0)=1). - Vincenzo Librandi, Dec 02 2010
G.f.: (14*x^2 - 23*x - 1)/(x - 1)^3. - Harvey P. Dale, May 07 2023
From Elmo R. Oliveira, Oct 25 2024: (Start)
E.g.f.: (5*x^2 + 25*x + 1)*exp(x).
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)
MATHEMATICA
lst={}; Do[a=5*n^2+20*n+1; AppendTo[lst, a], {n, 0, 5!}]; lst
Table[5n^2+20n+1, {n, 0, 40}] (* or *) LinearRecurrence[{3, -3, 1}, {1, 26, 61}, 40] (* or *) CoefficientList[Series[(14x^2-23x-1)/(x-1)^3, {x, 0, 40}], x] (* Harvey P. Dale, May 07 2023 *)
PROG
(Magma) [ 5*n^2+20*n+1: n in [0..50] ];
(PARI) a(n)=5*n^2+20*n+1 \\ Charles R Greathouse IV, Jun 17 2017
CROSSREFS
KEYWORD
easy,nonn,changed
AUTHOR
Pierre Gayet, Jul 01 2009
STATUS
approved