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 A232990 #40 Dec 12 2023 07:45:38
%S A232990 1,0,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,0,1,
%T A232990 0,1,0,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,0,
%U A232990 1,0,1,0,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0
%N A232990 Period 5: repeat [1,0,0,1,0].
%C A232990 Used by R. J. Baxter in studying the Rogers-Ramanujan identities.
%D A232990 Andrews, George E., q-series: their development and application in analysis, number theory, combinatorics, physics, and computer algebra. CBMS Regional Conference Series in Mathematics, 66. Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 1986. xii+130 pp. ISBN: 0-8218-0716-1 MR0858826 (88b:11063). See p. 105.
%H A232990 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,1).
%F A232990 a(n) = A198517(n+2).
%F A232990 a(n) = 2 + floor(n/5) - ceiling(n/5) + floor((n - 3)/5) - ceiling((n - 3)/5). - _Wesley Ivan Hurt_, Mar 13 2014
%F A232990 G.f.: -(x + 1)*(x^2 - x + 1)/((x - 1)*(x^4 + x^3 + x^2 + x + 1)). - _Colin Barker_, Mar 14 2014
%F A232990 a(n) = floor(((2*n - 2) mod 5)/3). - _Wesley Ivan Hurt_, Apr 30 2015
%F A232990 a(n) = (2/5)*(1 + cos(2*(n-3)*Pi/5) + cos(4*(n-3)*Pi/5) + cos(2*n*Pi/5) + cos(4*n*Pi/5)). - _Wesley Ivan Hurt_, Sep 26 2018
%p A232990 A232990:=n->2 + floor(n/5) - ceil(n/5) + floor((n-3)/5) - ceil((n-3)/5); # _Wesley Ivan Hurt_, Mar 13 2014
%t A232990 Table[2 + Floor[n/5] - Ceiling[n/5] + Floor[(n - 3)/5] - Ceiling[(n - 3)/5], {n, 0, 100}] (* _Wesley Ivan Hurt_, Mar 13 2014 *)
%o A232990 (PARI) Vec(-(x+1)*(x^2-x+1)/((x-1)*(x^4+x^3+x^2+x+1)) + O(x^100)) \\ _Colin Barker_, Mar 14 2014
%o A232990 (PARI) a(n)=((2*n-2)%5)\3 \\ _Charles R Greathouse IV_, Apr 30 2015
%o A232990 (Magma) /* By definition: */ &cat [[1,0,0,1,0]: n in [0..20]]; // _Bruno Berselli_, Feb 18 2015
%o A232990 (Magma) [(((n+1) mod 5) mod 3) mod 2: n in [0..100]]; // _Vincenzo Librandi_, Feb 18 2015
%Y A232990 Cf. A198517, A232991.
%K A232990 nonn,easy
%O A232990 0,1
%A A232990 _N. J. A. Sloane_, Dec 13 2013