A017138 a(n) = (8*n+6)^2.

36, 196, 484, 900, 1444, 2116, 2916, 3844, 4900, 6084, 7396, 8836, 10404, 12100, 13924, 15876, 17956, 20164, 22500, 24964, 27556, 30276, 33124, 36100, 39204, 42436, 45796, 49284, 52900, 56644, 60516, 64516, 68644, 72900, 77284, 81796, 86436, 91204, 96100, 101124

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• changed

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. A006752, A016838, A017137.

Programs

Magma

[(8*n+6)^2: n in [0..35]]; // Vincenzo Librandi, Jul 22 2011

Mathematica

Table[(8*n + 6)^2, {n, 0, 30}] (* Amiram Eldar, Apr 26 2023 *)

PARI

a(n)=(8*n+6)^2 \\ Charles R Greathouse IV, Jun 17 2017

Formula

G.f.: ( -36-88*x-4*x^2 ) / (x-1)^3. - R. J. Mathar, Aug 26 2015

From Amiram Eldar, Apr 26 2023: (Start)

a(n) = A017137(n)^2.

a(n) = 2^2*A016838(n).

Sum_{n>=0} 1/a(n) = Pi^2/64 - G/8, where G is Catalan's constant (A006752). (End)

E.g.f.: 4*exp(x)*(9 + 40*x + 16*x^2). - Stefano Spezia, Sep 02 2025