login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A017270
a(n) = (10*n)^2.
4
0, 100, 400, 900, 1600, 2500, 3600, 4900, 6400, 8100, 10000, 12100, 14400, 16900, 19600, 22500, 25600, 28900, 32400, 36100, 40000, 44100, 48400, 52900, 57600, 62500, 67600, 72900, 78400, 84100, 90000, 96100, 102400, 108900, 115600, 122500, 129600, 136900, 144400
OFFSET
0,2
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.
a(n) = A008592(n)^2 = A000290(A008592(n)) = A016850(2*n). (End)
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
STATUS
approved