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 A027689 #41 Oct 28 2024 18:46:56
%S A027689 4,6,10,16,24,34,46,60,76,94,114,136,160,186,214,244,276,310,346,384,
%T A027689 424,466,510,556,604,654,706,760,816,874,934,996,1060,1126,1194,1264,
%U A027689 1336,1410,1486,1564,1644,1726,1810,1896,1984,2074,2166,2260,2356,2454,2554
%N A027689 a(n) = n^2 + n + 4.
%H A027689 Muniru A Asiru, <a href="/A027689/b027689.txt">Table of n, a(n) for n = 0..2000</a>
%H A027689 Patrick De Geest, <a href="http://www.worldofnumbers.com/quasimor.htm">Palindromic Quasi_Over_Squares of the form n^2+(n+X)</a>.
%H A027689 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A027689 a(n) = A000217(n-2) + A000217(n+2) for n > 0. - _Jon Perry_, Jul 23 2003
%F A027689 a(n) = 2*n + a(n-1)-2 (with a(1)=4). - _Vincenzo Librandi_, Aug 05 2010
%F A027689 Sum_{n>=0} 1/a(n) = Pi*tanh(Pi*sqrt(15)/2)/sqrt(15). - _Amiram Eldar_, Jan 18 2021
%F A027689 From _Elmo R. Oliveira_, Oct 28 2024: (Start)
%F A027689 G.f.: 2*(2 - 3*x + 2*x^2)/(1 - x)^3.
%F A027689 E.g.f.: (2*(2 + x) + x^2)*exp(x).
%F A027689 a(n) = 2*A152948(n+2). (End)
%p A027689 with (combinat):seq(fibonacci(3, n)+n+3, n=0..47); # _Zerinvary Lajos_, Jun 07 2008
%t A027689 Table[n^2+n+4,{n,0,100}] (* _Vladimir Joseph Stephan Orlovsky_, Feb 17 2011 *)
%t A027689 LinearRecurrence[{3,-3,1},{4,6,10},50] (* or *) CoefficientList[ Series[ (-4+6*x-4*x^2)/(-1+x)^3,{x,0,50}],x] (* _Harvey P. Dale_, Dec 18 2021 *)
%o A027689 (PARI) a(n)=n^2+n+4 \\ _Charles R Greathouse IV_, Oct 07 2015
%o A027689 (GAP) List([0..50],n->n^2+n+4); # _Muniru A Asiru_, Jul 15 2018
%Y A027689 Cf. A000217, A002522, A152948.
%K A027689 nonn,easy
%O A027689 0,1
%A A027689 _Patrick De Geest_