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 A027690 #39 Oct 30 2024 16:50:37
%S A027690 5,7,11,17,25,35,47,61,77,95,115,137,161,187,215,245,277,311,347,385,
%T A027690 425,467,511,557,605,655,707,761,817,875,935,997,1061,1127,1195,1265,
%U A027690 1337,1411,1487,1565,1645,1727,1811,1897,1985,2075,2167,2261,2357,2455,2555
%N A027690 a(n) = n^2 + n + 5.
%H A027690 Patrick De Geest, <a href="http://www.worldofnumbers.com/quasimor.htm">Palindromic Quasi_Over_Squares of the form n^2+(n+X)</a>.
%H A027690 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A027690 a(n) = A176271(n+1,3) for n > 1. - _Reinhard Zumkeller_, Apr 13 2010
%F A027690 a(n) = 2*n + a(n-1) for n > 0, a(0)=5. - _Vincenzo Librandi_, Aug 05 2010
%F A027690 From _Ilya Gutkovskiy_, Nov 25 2016: (Start)
%F A027690 G.f.: (5 - 8*x + 5*x^2)/(1 - x)^3.
%F A027690 Sum_{n>=0} 1/a(n) = Pi*tanh(sqrt(19)*Pi/2)/sqrt(19) = 0.720729156259... (End)
%F A027690 From _Elmo R. Oliveira_, Oct 28 2024: (Start)
%F A027690 E.g.f.: (5 + 2*x + x^2)*exp(x).
%F A027690 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)
%p A027690 with(combinat): seq(fibonacci(3, n)+n+4, n=0..47); # _Zerinvary Lajos_, Jun 07 2008
%t A027690 Table[n^2 + n + 5, {n, 0, 100}] (* _T. D. Noe_, Oct 29 2009 *)
%o A027690 (PARI) a(n)=n^2+n+5 \\ _Charles R Greathouse IV_, Oct 07 2015
%Y A027690 Cf. A002061, A002522, A176271.
%K A027690 nonn,easy
%O A027690 0,1
%A A027690 _Patrick De Geest_
%E A027690 Corrected by _T. D. Noe_, Nov 09 2006
%E A027690 Definition and offset fixed by _Franklin T. Adams-Watters_, Jul 06 2009