A155449 Numbers k == 6 or 11 (mod 17).

6, 11, 23, 28, 40, 45, 57, 62, 74, 79, 91, 96, 108, 113, 125, 130, 142, 147, 159, 164, 176, 181, 193, 198, 210, 215, 227, 232, 244, 249, 261, 266, 278, 283, 295, 300, 312, 317, 329, 334, 346, 351, 363, 368, 380, 385, 397, 402, 414, 419, 431, 436, 448, 453

Offset: 1

Author

Vincenzo Librandi, Jan 22 2009

Keywords

• nonn
• easy

Comments

Or, numbers k such that k^2 == 2 (mod 17).

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Programs

Mathematica

LinearRecurrence[{1,1,-1},{6,11,23},100] (* Vincenzo Librandi, Feb 29 2012 *)
CoefficientList[Series[(6 + 5 x + 6 x^2)/((1 + x) (1 - x)^2), {x, 0, 60}], x] (* Vincenzo Librandi, May 03 2014 *)

Formula

a(n) = a(n-1) + a(n-2) - a(n-3); a(1)=6, a(2)=11, a(3)=23.

G.f.: x*(6 + 5*x + 6*x^2)/((1 + x)*(1 - x)^2). - Vincenzo Librandi, May 03 2014

Sum_{n>=1} (-1)^(n+1)/a(n) = tan(5*Pi/34)*Pi/17. - Amiram Eldar, Feb 27 2023

Extensions

Simpler definition from Franklin T. Adams-Watters, Jun 16 2010