OFFSET
0,1
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
From G. C. Greubel, Jan 13 2018: (Start)
G.f.: (11 - 21*x + 12*x^2)/(1 - x)^3.
E.g.f.: (11 + x + x^2)*exp(x). (End)
From Amiram Eldar, Nov 02 2020: (Start)
Sum_{n>=0} 1/a(n) = (1 + sqrt(11)*Pi*coth(sqrt(11)*Pi))/22.
Sum_{n>=0} (-1)^n/a(n) = (1 + sqrt(11)*Pi*cosech(sqrt(11)*Pi))/22. (End)
From Amiram Eldar, Feb 12 2024: (Start)
Product_{n>=0} (1 - 1/a(n)) = sqrt(10/11)*sinh(sqrt(10)*Pi)/sinh(sqrt(11)*Pi).
Product_{n>=0} (1 + 1/a(n)) = 2*sqrt(3/11)*sinh(2*sqrt(3)*Pi)/sinh(sqrt(11)*Pi). (End)
MATHEMATICA
Table[n^2+11, {n, 0, 100}]
LinearRecurrence[{3, -3, 1}, {11, 12, 15}, 60] (* Harvey P. Dale, Aug 24 2020 *)
PROG
(PARI) a(n)=n^2+11 \\ Charles R Greathouse IV, Jun 17 2017
(Magma) [n^2 + 11: n in [0..50]]; // G. C. Greubel, Jan 13 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vladimir Joseph Stephan Orlovsky, Apr 28 2011
STATUS
approved