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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 (list; graph; refs; listen; history; text; internal format)
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)/(1-x^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

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Last modified December 14 19:27 EST 2019. Contains 329987 sequences. (Running on oeis4.)