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 A027694 #40 Oct 30 2024 16:52:44
%S A027694 9,11,15,21,29,39,51,65,81,99,119,141,165,191,219,249,281,315,351,389,
%T A027694 429,471,515,561,609,659,711,765,821,879,939,1001,1065,1131,1199,1269,
%U A027694 1341,1415,1491,1569,1649,1731,1815,1901,1989,2079,2171,2265,2361,2459,2559
%N A027694 a(n) = n^2 + n + 9.
%H A027694 Patrick De Geest, <a href="http://www.worldofnumbers.com/quasimor.htm">Palindromic Quasi_Over_Squares of the form n^2+(n+X)</a>.
%H A027694 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A027694 For n > 3, a(n) = A176271(n+1,5). - _Reinhard Zumkeller_, Apr 13 2010
%F A027694 G.f.: (-9 + 16*x - 9*x^2)/(x-1)^3. - _R. J. Mathar_, Feb 07 2011
%F A027694 a(0) = 9, a(n) = a(n-1) + 2*n. - _Vincenzo Librandi_, Feb 07 2011
%F A027694 Sum_{n>=0} 1/a(n) = Pi*tanh(Pi*sqrt(35)/2)/sqrt(35). - _Amiram Eldar_, Jan 17 2021
%F A027694 From _Elmo R. Oliveira_, Oct 28 2024: (Start)
%F A027694 E.g.f.: exp(x)*(9 + 2*x + x^2).
%F A027694 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)
%p A027694 with (combinat):seq(fibonacci(3, n)+n+8, n=0..46); # _Zerinvary Lajos_, Jun 07 2008
%t A027694 Table[n^2+n+9,{n,0,50}] (* _Harvey P. Dale_, Feb 07 2011 *)
%o A027694 (PARI) a(n)=n^2+n+9 \\ _Charles R Greathouse IV_, Oct 07 2015
%Y A027694 Cf. A002522, A176271.
%K A027694 nonn,easy
%O A027694 0,1
%A A027694 _Patrick De Geest_