%I #18 Sep 08 2022 08:46:07

%S 15,16,19,24,31,40,51,64,79,96,115,136,159,184,211,240,271,304,339,

%T 376,415,456,499,544,591,640,691,744,799,856,915,976,1039,1104,1171,

%U 1240,1311,1384,1459,1536,1615,1696,1779,1864,1951,2040,2131,2224,2319

%N a(n) = n^2 + 15.

%H Vincenzo Librandi, <a href="/A241750/b241750.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 (3,-3,1).

%F G.f.: (15 - 29*x + 16*x^2)/(1 - x)^3.

%F a(n) = a(-n) = 3*a(n-1) - 3*a(n-2) + a(n-3) = a(n-1) + 2*n - 1.

%F From _Amiram Eldar_, Nov 03 2020: (Start)

%F Sum_{n>=0} 1/a(n) = (1 + sqrt(15)*Pi*coth(sqrt(15)*Pi))/30.

%F Sum_{n>=0} (-1)^n/a(n) = (1 + sqrt(15)*Pi*cosech(sqrt(15)*Pi))/30. (End)

%t Table[n^2 + 15, {n, 0, 60}]

%o (Magma) [n^2+15: n in [0..60]];

%o (PARI) a(n)=n^2+15 \\ _Charles R Greathouse IV_, Jun 17 2017

%Y Cf. similar sequences listed in A114962.

%K nonn,easy

%O 0,1

%A _Vincenzo Librandi_, May 01 2014