A167533 a(n) = 71*n - a(n-1) for n>0, a(0)=12.

12, 59, 83, 130, 154, 201, 225, 272, 296, 343, 367, 414, 438, 485, 509, 556, 580, 627, 651, 698, 722, 769, 793, 840, 864, 911, 935, 982, 1006, 1053, 1077, 1124, 1148, 1195, 1219, 1266, 1290, 1337, 1361, 1408, 1432, 1479, 1503, 1550, 1574, 1621, 1645

Offset: 0

Author

Vincenzo Librandi, Nov 06 2009

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Programs

Magma

[(71/4)-(23/4)*(-1)^n+(71/2)*n: n in [0..50]]; // Vincenzo Librandi, Jun 06 2014

Mathematica

CoefficientList[Series[(12 + 47 x + 12 x^2)/((1 + x) (1 - x)^2), {x, 0, 50}], x] (* Vincenzo Librandi, Jun 06 2014 *)
LinearRecurrence[{1,1,-1},{12,59,83},50] (* Harvey P. Dale, Dec 09 2015 *)

Formula

G.f.: (12 + 47*x + 12*x^2)/((1 + x)*(1 - x)^2). - Vincenzo Librandi, Jun 06 2014

Sum_{n>=0} (-1)^n/a(n) = cot(12*Pi/71)*Pi/71. - Amiram Eldar, Feb 24 2023

Extensions

Edited by N. J. A. Sloane, Jun 23 2010