A017270 a(n) = (10*n)^2.

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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A000290, A008592, A016850.

Programs

Magma

[(10*n)^2: n in [0..40]]; // Vincenzo Librandi, Jul 28 2011

Mathematica

LinearRecurrence[{3,-3,1},{0,100,400},40] (* Harvey P. Dale, Oct 02 2017 *)

PARI

a(n)=(10*n)^2 \\ Charles R Greathouse IV, Jun 17 2017

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)