%I #28 Mar 19 2024 09:32:32

%S 12,59,83,130,154,201,225,272,296,343,367,414,438,485,509,556,580,627,

%T 651,698,722,769,793,840,864,911,935,982,1006,1053,1077,1124,1148,

%U 1195,1219,1266,1290,1337,1361,1408,1432,1479,1503,1550,1574,1621,1645

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

%H Vincenzo Librandi, <a href="/A167533/b167533.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).

%F G.f.: (12 + 47*x + 12*x^2)/((1 + x)*(1 - x)^2). - _Vincenzo Librandi_, Jun 06 2014

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

%t CoefficientList[Series[(12 + 47 x + 12 x^2)/((1 + x) (1 - x)^2), {x, 0, 50}], x] (* _Vincenzo Librandi_, Jun 06 2014 *)

%t LinearRecurrence[{1,1,-1},{12,59,83},50] (* _Harvey P. Dale_, Dec 09 2015 *)

%o (Magma) [(71/4)-(23/4)*(-1)^n+(71/2)*n: n in [0..50]]; // _Vincenzo Librandi_, Jun 06 2014

%K nonn,easy

%O 0,1

%A _Vincenzo Librandi_, Nov 06 2009

%E Edited by _N. J. A. Sloane_, Jun 23 2010