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%I #15 Jun 13 2015 00:51:08
%S 1,1,1,4,2,2,7,3,3,10,4,4,13,5,5,16,6,6,19,7,7,22,8,8,25,9,9,28,10,10,
%T 31,11,11,34,12,12,37,13,13,40,14,14,43,15,15,46,16,16,49,17,17,52,18,
%U 18,55,19,19,58,20,20,61,21,21,64,22,22,67,23,23,70,24,24,73,25,25,76
%N #{0<=k<=n: k*n is divisible by 3}.
%H Colin Barker, <a href="/A087507/b087507.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 (0,0,2,0,0,-1).
%F a(n) = sum{k=0..n, if (mod(kn, 3)=0, 1, 0) }.
%F a(n) = floor(n/3)(5/3+4/3cos(2Pi*/3))+1.
%F a(n)+A087508(n)+A087509(n) = n.
%F a(n) = 2*a(n-3)-a(n-6) for n>5. - _Colin Barker_, May 02 2015
%F G.f.: (2*x^3+x^2+x+1) / ((x-1)^2*(x^2+x+1)^2). - _Colin Barker_, May 02 2015
%o (PARI) Vec((2*x^3+x^2+x+1)/((x-1)^2*(x^2+x+1)^2) + O(x^100)) \\ _Colin Barker_, May 02 2015
%Y Cf. A016777 (trisection).
%K easy,nonn
%O 0,4
%A _Paul Barry_, Sep 11 2003
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