OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
a(n) = a(n-1) + 200*n - 100, n > 0 ; a(0)=0. - Miquel Cerda, Oct 30 2016
G.f.: 100*x*(1 + x)/(1 - x)^3. - Ilya Gutkovskiy, Oct 30 2016
a(n) = 100*A000290(n). - Michel Marcus, Oct 30 2016
From Amiram Eldar, Jan 25 2021: (Start)
Sum_{n>=1} 1/a(n) = Pi^2/600.
Sum_{n>=1} (-1)^(n+1)/a(n) = Pi^2/1200.
Product_{n>=1} (1 + 1/a(n)) = sinh(Pi/10)/(Pi/10).
Product_{n>=1} (1 - 1/a(n)) = sin(Pi/10)/(Pi/10) = 5*(sqrt(5)-1)/(2*Pi). (End)
From Elmo R. Oliveira, Nov 30 2024: (Start)
E.g.f.: 100*x*(1 + x)*exp(x).
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2.
MATHEMATICA
LinearRecurrence[{3, -3, 1}, {0, 100, 400}, 40] (* Harvey P. Dale, Oct 02 2017 *)
PROG
(Magma) [(10*n)^2: n in [0..40]]; // Vincenzo Librandi, Jul 28 2011
(PARI) a(n)=(10*n)^2 \\ Charles R Greathouse IV, Jun 17 2017
CROSSREFS
KEYWORD
nonn,easy,changed
AUTHOR
STATUS
approved