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 A286716 #16 May 19 2017 06:02:28 %S A286716 0,0,1,1,1,1,2,2,3,2,3,3,4,4,4,4,5,5,6,5,6,6,7,7,7,7,8,8,9,8,9,9,10, %T A286716 10,10,10,11,11,12,11,12,12,13,13,13,13,14,14,15,14,15,15,16,16,16,16, %U A286716 17,17,18,17,18,18,19,19,19,19,20,20,21,20,21,21,22 %N A286716 a(n) = floor(n/2) - floor((n+1)/5), n >= 0. %C A286716 This is the number of integers k in the (left-sided open) interval ((n+1)/5, floor(n/2)]. This sequence is used in A286717(n), the number of zeros of Chebyshev's S(n, x) polynomial (A049310) in the open interval (-phi, +phi), with phi = (1 + sqrt(5))/2 (golden section) = A001622. %H A286716 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,0,0,1,0,-1). %F A286716 G.f.: x^2*(1 + x + x^4)/((1-x^2)*(1-x^5)). %F A286716 a(n) = a(n-2) + a(n-5) - a(n-7) for n>6. - _Colin Barker_, May 18 2017 %o A286716 (PARI) concat(vector(2), Vec(x^2*(1 + x + x^4) / ((1 - x)^2*(1 + x)*(1 + x + x^2 + x^3 + x^4)) + O(x^100))) \\ _Colin Barker_, May 18 2017 %Y A286716 Cf. A049310, A059169, A285870, A286717. %K A286716 nonn,easy %O A286716 0,7 %A A286716 _Wolfdieter Lang_, May 13 2017