%I
%S 1,2,0,3,4,0,5,6,0,7,8,0,9,10,0,11,12,0,13,14,0,15,16,0,17,18,0,19,20,
%T 0,21,22,0,23,24,0,25,26,0,27,28,0,29,30,0,31,32,0,33,34,0,35,36,0,37,
%U 38,0,39,40,0,41,42,0,43,44,0,45,46,0,47,48,0,49,50,0,51,52,0,53,54,0
%N Count, inserting 0 after every even number.
%C Row sums of A117908.
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,2,0,0,1)
%F G.f.: (1+2x+x^3)/(1x^3)^2.
%F a(n) = Sum_{k=0..n} 0^abs(L(C(n,2)/3)2*L(C(k,2)/3)) where L(j/p) is the Legendre symbol of j and p.
%F a(n) = sin((n+1)*Pi/3)*((8n+14)*sin((n+1)*Pi/3)sqrt(3)*cos(n*Pi))/9.  _Wesley Ivan Hurt_, Sep 24 2017
%t Riffle[Range[60],0,3] (* _Harvey P. Dale_, Sep 12 2013 *)
%Y Cf. A009947, A117908.
%K easy,nonn
%O 0,2
%A _Paul Barry_, Apr 01 2006
