A017522 a(n) = (12*n)^2.

0, 144, 576, 1296, 2304, 3600, 5184, 7056, 9216, 11664, 14400, 17424, 20736, 24336, 28224, 32400, 36864, 41616, 46656, 51984, 57600, 63504, 69696, 76176, 82944, 90000, 97344, 104976, 112896, 121104, 129600, 138384, 147456, 156816, 166464, 176400, 186624, 197136

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A000290 (n^2), A008594 (12*n).

Programs

Magma

[(12*n)^2: n in [0..35]]; // Vincenzo Librandi, Feb 10 2012

Mathematica

LinearRecurrence[{3, -3, 1}, {0, 144, 576}, 50] (* Vincenzo Librandi, Feb 10 2012 *)
(12 Range[0, 30])^2 (* Bruno Berselli, Feb 10 2012 *)

PARI

a(n)=(12*n)^2 \\ Charles R Greathouse IV, Jun 17 2017

Formula

G.f.: 144*x*(1+x)/(1-x)^3. - Bruno Berselli, Feb 10 2012

From Amiram Eldar, Jan 25 2021: (Start)

Sum_{n>=1} 1/a(n) = Pi^2/864.

Sum_{n>=1} (-1)^(n+1)/a(n) = Pi^2/1728.

Product_{n>=1} (1 + 1/a(n)) = sinh(Pi/12)/(Pi/12).

Product_{n>=1} (1 - 1/a(n)) = sin(Pi/12)/(Pi/12) = 3*sqrt(2)*(sqrt(3)-1)/Pi. (End)

From Elmo R. Oliveira, Dec 02 2024: (Start)

E.g.f.: 144*x*(1 + x)*exp(x).

a(n) = 144*A000290(n) = A008594(n)^2 = A000290(A008594(n)).

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)