A001538 a(n) = (12*n+1)*(12*n+11).

11, 299, 875, 1739, 2891, 4331, 6059, 8075, 10379, 12971, 15851, 19019, 22475, 26219, 30251, 34571, 39179, 44075, 49259, 54731, 60491, 66539, 72875, 79499, 86411, 93611, 101099, 108875, 116939, 125291, 133931, 142859, 152075, 161579, 171371, 181451, 191819

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. A001533, A017533, A017653.

Programs

Mathematica

Table[(12n+1)(12n+11),{n,0,40}] (* or *) LinearRecurrence[{3,-3,1},{11,299,875},40] (* Harvey P. Dale, Jul 22 2024 *)

PARI

a(n)=(12*n+1)*(12*n+11) \\ Charles R Greathouse IV, Jun 16 2017

Formula

a(n) = (9*A001533(n) - 19)/4.

a(n) = 288*n + a(n-1) with a(0)=11. - Vincenzo Librandi, Nov 12 2010

G.f.: -(11 + 266*x + 11*x^2)/(x-1)^3. - R. J. Mathar, Jun 30 2020

From Amiram Eldar, Feb 20 2023: (Start)

a(n) = A017533(n)*A017653(n).

Sum_{n>=0} 1/a(n) = (sqrt(3)+2)*Pi/120.

Sum_{n>=0} (-1)^n/a(n) = (4*log(sqrt(2)+1) + sqrt(3)*log(5+2*sqrt(6)))/(60*sqrt(2)).

Product_{n>=0} (1 - 1/a(n)) = (2*sqrt(2)/(sqrt(3)-1))*cos(sqrt(13/2)*Pi/6).

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

From Elmo R. Oliveira, Oct 25 2024: (Start)

E.g.f.: exp(x)*(11 + 144*x*(2 + x)).

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