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 A082108 #49 Dec 22 2022 02:11:07
%S A082108 1,11,29,55,89,131,181,239,305,379,461,551,649,755,869,991,1121,1259,
%T A082108 1405,1559,1721,1891,2069,2255,2449,2651,2861,3079,3305,3539,3781,
%U A082108 4031,4289,4555,4829,5111,5401,5699,6005,6319,6641,6971,7309,7655,8009,8371
%N A082108 a(n) = 4*n^2 + 6*n + 1.
%C A082108 a(n) is the sum of the numerator and denominator of (n+1)/(2*n) + (n+2)/(2*(n+1)); all fractions are reduced and n > 0. - _J. M. Bergot_, Jun 14 2017
%H A082108 G. C. Greubel, <a href="/A082108/b082108.txt">Table of n, a(n) for n = 0..1000</a>
%H A082108 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A082108 a(n) = a(n-1) + 8*n + 2. - _Vincenzo Librandi_, Aug 08 2010
%F A082108 From _Michael De Vlieger_, Jun 15 2017: (Start)
%F A082108 G.f.: (1 + 8*x - x^2)/(1 - x)^3.
%F A082108 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). (End)
%F A082108 a(n) = A016742(n) + A008588(n) + 1. - _Felix Fröhlich_, Jun 16 2017
%F A082108 Sum_{k=1..n} a(k-1)/(2*k)! = 1 - 1/(2*n)!. - _Robert Israel_, Jul 19 2017
%F A082108 E.g.f.: (1 + 10*x + 4*x^2)*exp(x). - _G. C. Greubel_, Dec 22 2022
%t A082108 (* Programs from _Michael De Vlieger_, Jun 15 2017 *)
%t A082108 Table[4n^2 +6n +1, {n,0,50}]
%t A082108 LinearRecurrence[{3,-3,1}, {1,11,29}, 51]
%t A082108 CoefficientList[Series[(1+8*x-x^2)/(1-x)^3, {x,0,50}], x] (* End *)
%o A082108 (PARI) a(n)=4*n^2+6*n+1 \\ _Charles R Greathouse IV_, Oct 07 2015
%o A082108 (Magma) [4*n^2+6*n+1: n in [0..60]]; // _G. C. Greubel_, Dec 22 2022
%o A082108 (SageMath) [4*n^2+6*n+1 for n in range(61)] # _G. C. Greubel_, Dec 22 2022
%Y A082108 Cf. A028387, A069131.
%K A082108 easy,nonn
%O A082108 0,2
%A A082108 _Paul Barry_, Apr 03 2003
%E A082108 Incorrect formula and useless examples deleted by _R. J. Mathar_, Aug 31 2010