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 A082106 #18 Jan 08 2023 02:42:09
%S A082106 1,6,33,118,321,726,1441,2598,4353,6886,10401,15126,21313,29238,39201,
%T A082106 51526,66561,84678,106273,131766,161601,196246,236193,281958,334081,
%U A082106 393126,459681,534358,617793,710646,813601,927366,1052673,1190278,1340961,1505526,1684801
%N A082106 Main diagonal of number array A082105.
%C A082106 4*a(n) can be written as (n^2 + 2*n + 1)^2 + (n^2 - 2*n + 1)^2 + (n^2 - 2*n - 1)^2 + (n^2 + 2*n - 1)^2. - _Bruno Berselli_, Jun 20 2014
%H A082106 G. C. Greubel, <a href="/A082106/b082106.txt">Table of n, a(n) for n = 0..1000</a>
%H A082106 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F A082106 a(n) = n^4 + 4*n^2 + 1.
%F A082106 a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5). - _Harvey P. Dale_, Dec 06 2012
%F A082106 G.f.: (1 + x + 13*x^2 + 3*x^3 + 6*x^4)/(1 - x)^5. - _Bruno Berselli_, Jun 20 2014
%F A082106 E.g.f.: (1 + 5*x + 11*x^2 + 6*x^3 + x^4)*exp(x). - _G. C. Greubel_, Dec 22 2022
%F A082106 Sum_{n>=0} 1/a(n) = 1/2 + (Pi/4)*((1/sqrt(2)+1/sqrt(6))*coth(sqrt(2-sqrt(3))*Pi) - (1/sqrt(2)-1/sqrt(6))*coth(sqrt(2+sqrt(3))*Pi)). - _Amiram Eldar_, Jan 08 2023
%t A082106 Table[n^4+4n^2+1,{n,0,40}] (* or *) LinearRecurrence[{5,-10,10,-5,1},{1,6,33,118,321},40] (* _Harvey P. Dale_, Dec 06 2012 *)
%o A082106 (Magma) [(n^2+2)^2 -3: n in [0..40]]; // _G. C. Greubel_, Dec 22 2022
%o A082106 (SageMath) [(n^2+2)^2 -3 for n in range(41)] # _G. C. Greubel_, Dec 22 2022
%Y A082106 Cf. A082047, A082044, A082105, A082107, A082109.
%K A082106 nonn,easy
%O A082106 0,2
%A A082106 _Paul Barry_, Apr 03 2003