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A117909 Count, inserting 0 after every even number. 1


%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)/(1-x^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

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Last modified January 18 01:05 EST 2020. Contains 330995 sequences. (Running on oeis4.)