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 A212669 #18 Dec 01 2015 09:49:27
%S A212669 18,340,2022,7400,20602,48060,99022,186064,325602,538404,850102,
%T A212669 1291704,1900106,2718604,3797406,5194144,6974386,9212148,11990406,
%U A212669 15401608,19548186,24543068,30510190,37585008,45915010,55660228,66993750,80102232,95186410,112461612
%N A212669 a(n) = 2/15 * (32*n^5 + 80*n^4 + 40*n^3 - 20*n^2 + 3*n).
%C A212669 a(n) is the difference between numbers of nonnegative multiples of 2*n+1 with even and odd digit sum in base 2*n in interval [0, 64*n^6).
%H A212669 Colin Barker, <a href="/A212669/b212669.txt">Table of n, a(n) for n = 1..1000</a>
%H A212669 V. Shevelev, <a href="http://arxiv.org/abs/0710.3177">On monotonic strengthening of Newman-like phenomenon on (2m+1)-multiples in base 2m</a>, arXiv:0710.3177 [math.NT], 2007.
%H A212669 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
%F A212669 a(n) = 2/(2*n+1)*Sum_{i=1..n} tan^6(Pi*i/(2*n+1)).
%F A212669 G.f.: 2*x*(9+116*x+126*x^2+4*x^3+x^4) / (1-x)^6. - _Colin Barker_, Dec 01 2015
%o A212669 (PARI) Vec(2*x*(9+116*x+126*x^2+4*x^3+x^4)/(1-x)^6 + O(x^50)) \\ _Colin Barker_, Dec 01 2015
%Y A212669 Cf. A038754, A084990, A091042, A212500, A212592, A212592, A212592, A212668.
%K A212669 nonn,base,easy
%O A212669 1,1
%A A212669 _Vladimir Shevelev_ and _Peter J. C. Moses_, May 23 2012