

A117909


Count, inserting 0 after every even number.


1



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, 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, 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
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OFFSET

0,2


COMMENTS

Row sums of A117908.


LINKS

Table of n, a(n) for n=0..80.
Index entries for linear recurrences with constant coefficients, signature (0,0,2,0,0,1)


FORMULA

G.f.: (1+2x+x^3)/(1x^3)^2.
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.
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


MATHEMATICA

Riffle[Range[60], 0, 3] (* Harvey P. Dale, Sep 12 2013 *)


CROSSREFS

Cf. A009947, A117908.
Sequence in context: A209705 A181289 A229032 * A261094 A091538 A013584
Adjacent sequences: A117906 A117907 A117908 * A117910 A117911 A117912


KEYWORD

easy,nonn


AUTHOR

Paul Barry, Apr 01 2006


STATUS

approved



