A241890 - OEIS

%I #17 Sep 08 2022 08:46:07

%S 24,25,28,33,40,49,60,73,88,105,124,145,168,193,220,249,280,313,348,

%T 385,424,465,508,553,600,649,700,753,808,865,924,985,1048,1113,1180,

%U 1249,1320,1393,1468,1545,1624,1705,1788,1873,1960,2049,2140,2233,2328

%N a(n) = n^2 + 24.

%H Vincenzo Librandi, <a href="/A241890/b241890.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.: (24 - 47*x + 25*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 04 2020: (Start)

%F Sum_{n>=0} 1/a(n) = (1 + sqrt(24)*Pi*coth(sqrt(24)*Pi))/48.

%F Sum_{n>=0} (-1)^n/a(n) = (1 + sqrt(24)*Pi*cosech(sqrt(24)*Pi))/48. (End)

%t Table[n^2 + 24, {n, 0, 60}]

%o (Magma) [n^2+24: n in [0..60]];

%o (PARI) a(n)=n^2+24 \\ _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