A017390 a(n) = (11*n)^2.

0, 121, 484, 1089, 1936, 3025, 4356, 5929, 7744, 9801, 12100, 14641, 17424, 20449, 23716, 27225, 30976, 34969, 39204, 43681, 48400, 53361, 58564, 64009, 69696, 75625, 81796, 88209, 94864, 101761, 108900, 116281, 123904, 131769, 139876, 148225, 156816, 165649, 174724

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, A008593.

Programs

Magma

[(11*n)^2: n in [0..40]]; // Vincenzo Librandi, Sep 02 2011

Mathematica

(11 Range[0,30])^2 (* or *) LinearRecurrence[{3,-3,1},{0,121,484},30] (* Harvey P. Dale, Nov 04 2021 *)

PARI

a(n)=(11*n)^2 \\ Charles R Greathouse IV, Jun 17 2017

Formula

From Amiram Eldar, Jan 25 2021: (Start)

Sum_{n>=1} 1/a(n) = Pi^2/726.

Sum_{n>=1} (-1)^(n+1)/a(n) = Pi^2/1452.

Product_{n>=1} (1 + 1/a(n)) = sinh(Pi/11)/(Pi/11).

Product_{n>=1} (1 - 1/a(n)) = sin(Pi/11)/(Pi/11). (End)

G.f.: -((121*x*(1+x))/(-1+x)^3). - Harvey P. Dale, Nov 04 2021

From Elmo R. Oliveira, Nov 30 2024: (Start)

E.g.f.: 121*x*(1 + x)*exp(x).

a(n) = 121*A000290(n) = A008593(n)^2.

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