A017066 a(n) = (8*n)^2.

0, 64, 256, 576, 1024, 1600, 2304, 3136, 4096, 5184, 6400, 7744, 9216, 10816, 12544, 14400, 16384, 18496, 20736, 23104, 25600, 28224, 30976, 33856, 36864, 40000, 43264, 46656, 50176, 53824, 57600, 61504, 65536, 69696, 73984, 78400, 82944, 87616, 92416, 97344, 102400

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, A008590, A016802, A152691, A244082.

Programs

Magma

[(8*n)^2: n in [0..35]]; // Vincenzo Librandi, Jul 10 2011

Mathematica

LinearRecurrence[{3, -3, 1}, {0, 64, 256}, 50] (* Vincenzo Librandi, Feb 10 2012 *)

PARI

a(n)=(8*n)^2 \\ Charles R Greathouse IV, Jun 17 2017

Formula

G.f.: -64*x*(1+x)/(x-1)^3. - R. J. Mathar, Jul 14 2016

a(n) = A000290(8*n) = A008590(n)^2 = A000290(A008590(n)).

From Amiram Eldar, Jan 25 2021: (Start)

Sum_{n>=1} 1/a(n) = Pi^2/384.

Sum_{n>=1} (-1)^(n+1)/a(n) = Pi^2/768.

Product_{n>=1} (1 + 1/a(n)) = sinh(Pi/8)/(Pi/8).

Product_{n>=1} (1 - 1/a(n)) = sin(Pi/8)/(Pi/8) = 4*sqrt(2-sqrt(2))/Pi. (End)

From Elmo R. Oliveira, Dec 06 2024: (Start)

E.g.f.: 64*exp(x)*x*(1 + x).

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

a(n) = n*A152691(n) = 2*A244082(n) = A016802(2*n). (End)