A001536 a(n) = (11*n+1)*(11*n+10).

10, 252, 736, 1462, 2430, 3640, 5092, 6786, 8722, 10900, 13320, 15982, 18886, 22032, 25420, 29050, 32922, 37036, 41392, 45990, 50830, 55912, 61236, 66802, 72610, 78660, 84952, 91486, 98262, 105280, 112540, 120042, 127786, 135772, 144000, 152470, 161182, 170136

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. A017401, A017509.

Programs

Mathematica

Table[(11*n + 1)*(11*n + 10), {n, 0, 40}] (* Amiram Eldar, Feb 20 2023 *)

PARI

a(n)=(11*n+1)*(11*n+10) \\ Charles R Greathouse IV, Jun 16 2017

Formula

a(n) = 242*n + a(n-1) with a(0)=10. - Vincenzo Librandi, Nov 12 2010

G.f.: -2*(5+111*x+5*x^2)/(x-1)^3. - R. J. Mathar, May 30 2022

From Amiram Eldar, Feb 20 2023: (Start)

a(n) = A017401(n)*A017509(n).

Sum_{n>=0} 1/a(n) = cot(Pi/11)*Pi/99.

Product_{n>=0} (1 - 1/a(n)) = cosec(Pi/11)*cos(sqrt(85)*Pi/22).

Product_{n>=0} (1 + 1/a(n)) = cosec(Pi/11)*cos(sqrt(77)*Pi/22). (End)

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

E.g.f.: exp(x)*(10 + 121*x*(2 + x)).

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