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 A261521 #76 Oct 20 2024 13:01:17
%S A261521 29,32,37,44,53,64,77,92,109,128,149,172,197,224,253,284,317,352,389,
%T A261521 428,469,512,557,604,653,704,757,812,869,928,989,1052,1117,1184,1253,
%U A261521 1324,1397,1472,1549,1628,1709,1792,1877,1964,2053,2144,2237,2332,2429,2528
%N A261521 a(n) = n^2 + 2*n + 29.
%C A261521 A139851, which lists primes of the form 4x^2 + 4xy + 29y^2, contains all prime values of a(n). - _Altug Alkan_, Oct 02 2015
%H A261521 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A261521 a(n) = a(n-1) + A005408(n), a(0) = 29, for n > 0. - _Altug Alkan_, Oct 02 2015
%F A261521 From _Vincenzo Librandi_, Oct 03 2015: (Start)
%F A261521 G.f.: (29 - 55*x + 28*x^2)/(1-x)^3.
%F A261521 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). (End)
%F A261521 a(n) = A005563(n) + 29. - _Omar E. Pol_, Oct 17 2015
%F A261521 E.g.f.: (29 + 3*x + x^2)*exp(x). - _Elmo R. Oliveira_, Oct 19 2024
%e A261521 For n = 3, a(3) = 3^2 + 2*3 + 29 = 44.
%t A261521 Table[n^2 + 2 n + 29, {n, 0, 50}] (* _Bruno Berselli_, Oct 25 2015 *)
%t A261521 LinearRecurrence[{3,-3,1},{29,32,37},50] (* _Harvey P. Dale_, Oct 14 2023 *)
%o A261521 (Python) def a(x):return x*x+2*x+27
%o A261521 (PARI) vector(50, n, n--; n^2+2*n+29) \\ _Altug Alkan_, Oct 02 2015
%o A261521 (PARI) Vec((29 - 55*x + 28*x^2)/(1-x)^3 + O(x^100)) \\ _Altug Alkan_, Oct 17 2015
%o A261521 (Magma) [n^2+2*n+29: n in [0..50]]; // _Vincenzo Librandi_, Oct 03 2015
%Y A261521 Cf. A005408, A005563, A139851.
%K A261521 nonn,easy
%O A261521 0,1
%A A261521 _Jake Saville_, Oct 02 2015