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 A285870 #15 Sep 08 2022 08:46:19
%S A285870 0,0,1,1,2,1,2,2,3,3,4,3,4,4,5,5,6,5,6,6,7,7,8,7,8,8,9,9,10,9,10,10,
%T A285870 11,11,12,11,12,12,13,13,14,13,14,14,15,15,16,15,16,16,17,17,18,17,18,
%U A285870 18,19,19,20,19,20,20,21,21,22,21,22,22,23,23,24
%N A285870 a(n) = floor(n/2) - floor((n+1)/6), n >= 0.
%C A285870 This is the number of integers k in the (left-sided open) interval ((n+1)/6, floor(n/2)]. This sequence is used in A285872(n), the number of zeros of Chebyshev's S(n, x) polynomial (A049310) in the open interval (-sqrt(3), +sqrt(3)).
%H A285870 G. C. Greubel, <a href="/A285870/b285870.txt">Table of n, a(n) for n = 0..5000</a>
%H A285870 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,1,-1).
%F A285870 a(n) = floor(n/2) - floor((n+1)/6), n >= 0.
%F A285870 G.f.: (x^2/((1+x)*(1-x)^2))*(1-x^3/((1+x+x^2)*(1-x+x^2))).
%F A285870 a(n) = a(n-1) + a(n-6) - a(n-7) for n>6. - _Colin Barker_, May 18 2017
%t A285870 Table[Floor[n/2] - Floor[(n + 1)/6], {n, 0, 60}] (* or *)
%t A285870 CoefficientList[Series[(x^2/((1 + x) (1 - x)^2)) (1 - x^3/((1 + x + x^2) (1 - x + x^2))), {x, 0, 60}], x] (* _Michael De Vlieger_, May 13 2017 *)
%o A285870 (Magma) [Floor(n/2)-Floor((n+1)/6): n in [0..100]]; // _Vincenzo Librandi_, May 15 2017
%o A285870 (PARI) concat(vector(2), Vec(x^2*(1 + x^2 - x^3 + x^4) / ((1 - x)^2*(1 + x)*(1 - x + x^2)*(1 + x + x^2)) + O(x^100))) \\ _Colin Barker_, May 18 2017
%Y A285870 Cf. A049310, A059169, A285869, A285872.
%K A285870 nonn,easy
%O A285870 0,5
%A A285870 _Wolfdieter Lang_, May 12 2017