This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A241851 #18 Nov 29 2024 19:08:13
%S A241851 21,22,25,30,37,46,57,70,85,102,121,142,165,190,217,246,277,310,345,
%T A241851 382,421,462,505,550,597,646,697,750,805,862,921,982,1045,1110,1177,
%U A241851 1246,1317,1390,1465,1542,1621,1702,1785,1870,1957,2046,2137,2230,2325,2422,2521
%N A241851 a(n) = n^2 + 21.
%H A241851 Vincenzo Librandi, <a href="/A241851/b241851.txt">Table of n, a(n) for n = 0..1000</a>
%H A241851 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A241851 G.f.: (21 - 41*x + 22*x^2)/(1 - x)^3.
%F A241851 a(n) = a(-n) = 3*a(n-1) - 3*a(n-2) + a(n-3) = a(n-1) + 2*n - 1.
%F A241851 From _Amiram Eldar_, Nov 04 2020: (Start)
%F A241851 Sum_{n>=0} 1/a(n) = (1 + sqrt(21)*Pi*coth(sqrt(21)*Pi))/42.
%F A241851 Sum_{n>=0} (-1)^n/a(n) = (1 + sqrt(21)*Pi*cosech(sqrt(21)*Pi))/42. (End)
%F A241851 E.g.f.: exp(x)*(21 + x + x^2). - _Elmo R. Oliveira_, Nov 29 2024
%t A241851 Table[n^2 + 21, {n, 0, 60}]
%o A241851 (Magma) [n^2+21: n in [0..60]];
%o A241851 (PARI) a(n)=n^2+21 \\ _Charles R Greathouse IV_, Jun 17 2017
%Y A241851 Cf. similar sequence listed in A114962.
%K A241851 nonn,easy
%O A241851 0,1
%A A241851 _Vincenzo Librandi_, May 01 2014