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 A289139 #23 Aug 10 2025 12:30:54
%S A289139 0,0,1,2,2,2,3,4,4,5,6,6,6,7,8,8,9,10,10,10,11,12,12,13,14,14,14,15,
%T A289139 16,16,17,18,18,18,19,20,20,21,22,22,22,23,24,24,25,26,26,26,27,28,28,
%U A289139 29,30,30,30,31,32,32,33,34,34,34,35,36,36,37,38,38,38,39,40,40
%N A289139 a(n) is the number of odd integers divisible by 7 in ]4*(n-1)^2, 4*n^2[.
%C A289139 This sequence has the form (0+4k,0+4k,1+4k,2+4k,2+4k,2+4k,3+4k) for k>=0.
%H A289139 Harvey P. Dale, <a href="/A289139/b289139.txt">Table of n, a(n) for n = 0..1000</a>
%H A289139 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,1,-1).
%F A289139 a(n + 7*k) = a(n) + 4*k.
%F A289139 G.f.: (x^7+x^6+x^3+x^2)/(x^8-x^7-x+1). - _Alois P. Heinz_, Jun 26 2017
%t A289139 Table[Count[Mod[Table[2(2(n-1)^2 +k)-1, {k,1,4 n-2}],7],0], {n,0,100}]
%t A289139 LinearRecurrence[{1,0,0,0,0,0,1,-1},{0,0,1,2,2,2,3,4},80] (* _Harvey P. Dale_, Aug 10 2025 *)
%Y A289139 Cf. A289120, A289133, A289122, A288156, A004523.
%K A289139 nonn,easy
%O A289139 0,4
%A A289139 _Ralf Steiner_, Jun 26 2017