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 A288156 #66 Jan 19 2025 12:58:48
%S A288156 0,0,1,1,1,2,2,3,3,3,4,4,5,5,5,6,6,7,7,7,8,8,9,9,9,10,10,11,11,11,12,
%T A288156 12,13,13,13,14,14,15,15,15,16,16,17,17,17,18,18,19,19,19,20,20,21,21,
%U A288156 21,22,22,23,23,23,24,24,25,25,25,26,26,27,27,27,28,28,29,29,29,30,30,31,31,31,32,32,33,33,33,34,34,35,35,35,36,36,37,37,37,38,38,39,39,39,40
%N A288156 Two even followed by three odd integers: the pattern is (0+2k, 0+2k, 1+2k, 1+2k, 1+2k) for k >= 0.
%C A288156 a(n) = number of odd integers divisible by 5 in the interval ]2*(n-1)^2, 2*n^2[.
%H A288156 Harvey P. Dale, <a href="/A288156/b288156.txt">Table of n, a(n) for n = 0..1000</a>
%H A288156 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,1,-1).
%F A288156 a(5*k + r) = floor((r + 3)/5) + 2*k for k >= 0 and r < 5. - _David A. Corneth_, Jun 25 2017
%F A288156 G.f.: x^2*(x^3+1)/(x^6-x^5-x+1) = x^2 *(1+x) *(1-x+x^2) /( (1-x)^2 * (1+x+x^2+x^3+x^4) ). - _Alois P. Heinz_, Jul 04 2017
%F A288156 From _Luce ETIENNE_, Feb 18 2020: (Start)
%F A288156 a(n) = 2*a(n-5) - a(n-10).
%F A288156 a(n) = a(n-1) + a(n-5) - a(n-6). (End)
%F A288156 a(n) = floor((2*n+1)/5) for n >= 0. - _Mones Kasem Jaafar_, Jun 25 2023
%F A288156 Sum_{n>=2} (-1)^n/a(n) = Pi/4. - _Amiram Eldar_, Jul 20 2023
%t A288156 Table[Count[Mod[Table[2 ((n - 1)^2 + k) - 1, {k, 1, 2 n - 1}], 5], 0], {n, 0, 100}]
%t A288156 LinearRecurrence[{1,0,0,0,1,-1},{0,0,1,1,1,2},120] (* _Harvey P. Dale_, Jan 19 2025 *)
%Y A288156 Cf. A004523.
%Y A288156 Two zeros followed by partial sums of A232990.
%K A288156 nonn,easy
%O A288156 0,6
%A A288156 _Ralf Steiner_, Jun 25 2017