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 A241749 #25 Apr 21 2025 10:46:09
%S A241749 13,14,17,22,29,38,49,62,77,94,113,134,157,182,209,238,269,302,337,
%T A241749 374,413,454,497,542,589,638,689,742,797,854,913,974,1037,1102,1169,
%U A241749 1238,1309,1382,1457,1534,1613,1694,1777,1862,1949,2038,2129,2222,2317,2414,2513
%N A241749 a(n) = n^2 + 13.
%C A241749 For i=0..28, 2*a(i) + 3 is prime. - _Vincenzo Librandi_, Jun 01 2014
%H A241749 Vincenzo Librandi, <a href="/A241749/b241749.txt">Table of n, a(n) for n = 0..1000</a>
%H A241749 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A241749 G.f.: (13 - 25*x + 14*x^2)/(1 - x)^3.
%F A241749 a(n) = a(-n) = 3*a(n-1) - 3*a(n-2) + a(n-3) = a(n-1) + 2*n - 1.
%F A241749 From _Amiram Eldar_, Nov 02 2020: (Start)
%F A241749 Sum_{n>=0} 1/a(n) = (1 + sqrt(13)*Pi*coth(sqrt(13)*Pi))/26.
%F A241749 Sum_{n>=0} (-1)^n/a(n) = (1 + sqrt(13)*Pi*cosech(sqrt(13)*Pi))/26. (End)
%F A241749 E.g.f.: exp(x)*(13 + x + x^2). - _Elmo R. Oliveira_, Apr 20 2025
%t A241749 Table[n^2 + 13, {n, 0, 60}]
%o A241749 (Magma) [n^2+13: n in [0..60]];
%o A241749 (PARI) a(n)=n^2+13 \\ _Charles R Greathouse IV_, Jun 17 2017
%Y A241749 Cf. similar sequences listed in A114962.
%K A241749 nonn,easy
%O A241749 0,1
%A A241749 _Vincenzo Librandi_, Apr 30 2014