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%I #11 Jul 04 2017 21:22:06
%S 0,0,2,2,2,4,4,6,6,6,8,8,10,10,10,12,12,14,14,14,16,16,18,18,18,20,20,
%T 22,22,22,24,24,26,26,26,28,28,30,30,30,32,32,34,34,34,36,36,38,38,38,
%U 40,40,42,42,42,44,44,46,46,46,48,48,50,50,50,52,52,54
%N a(n) is the number of odd integers divisible by 5 in ]4*(n-1)^2, 4*n^2[.
%C This sequence has the form (0+4k,0+4k,2+4k,2+4k,2+4k) for k>=0.
%H Colin Barker, <a href="/A289195/b289195.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,1,-1).
%F a(n + 5*k) = a(n) + 4*k.
%F From _Colin Barker_, Jul 04 2017: (Start)
%F G.f.: 2*x^2*(1 + x)*(1 - x + x^2) / ((1 - x)^2*(1 + x + x^2 + x^3 + x^4)).
%F a(n) = a(n-1) + a(n-5) - a(n-6) for n>5.
%F (End)
%t Table[Count[Mod[Table[2(2(n-1)^2+k)-1,{k,1,4 n-2}],5],0],{n,0,50}]
%o (PARI) concat(vector(2), Vec(2*x^2*(1 + x)*(1 - x + x^2) / ((1 - x)^2*(1 + x + x^2 + x^3 + x^4)) + O(x^100))) \\ _Colin Barker_, Jul 04 2017
%Y Cf. A289199, A289139, A289120, A289133, A289122, A288156, A004523.
%K nonn,easy
%O 0,3
%A _Ralf Steiner_, Jun 28 2017
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