A001513 a(n) = (6*n+1)*(6*n+5).

5, 77, 221, 437, 725, 1085, 1517, 2021, 2597, 3245, 3965, 4757, 5621, 6557, 7565, 8645, 9797, 11021, 12317, 13685, 15125, 16637, 18221, 19877, 21605, 23405, 25277, 27221, 29237, 31325, 33485, 35717, 38021, 40397, 42845, 45365, 47957, 50621, 53357, 56165, 59045

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A016921, A016969.

Programs

Mathematica

a[n_] := (6*n + 1)*(6*n + 5); Array[a, 40, 0] (* Amiram Eldar, Feb 19 2023 *)

PARI

a(n)=(6*n+1)*(6*n+5) \\ Charles R Greathouse IV, Jun 17 2017

Formula

Sum_{k>=0} 1/a(k) = Pi/(8*sqrt(3)) = 0.22672492... - Jaume Oliver Lafont, May 30 2010

a(n) = 72*n + a(n-1) with a(0)=5. - Vincenzo Librandi, Nov 12 2010

G.f.: (-5 - 62*x - 5*x^2) / (x-1)^3. - R. J. Mathar, Jan 19 2013

From Amiram Eldar, Feb 19 2023: (Start)

a(n) = A016921(n)*A016969(n).

Sum_{n>=0} (-1)^n/a(n) = log(2+sqrt(3))/(4*sqrt(3)).

Product_{n>=0} (1 - 1/a(n)) = 2*cos(sqrt(5)*Pi/6).

Product_{n>=0} (1 + 1/a(n)) = 2*cos(sqrt(3)*Pi/6). (End)