A117909 Count, inserting 0 after every even number.

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

Offset

0,2

Comments

Row sums of A117908.

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,0,2,0,0,-1)

Formula

G.f.: (1 +2*x +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)*((8*n+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 *)

Prog

(Magma) I:=[1, 2, 0, 3, 4, 0]; [n le 6 select I[n] else 2*Self(n-3) - Self(n-6): n in [1..91]]; // G. C. Greubel, Oct 21 2021
(Sage)
def a(n): return (2*n+3)/3 if (n%3==0) else 2*(n+2)/3 if (n%3==1) else 0
[a(n) for n in (0..90)] # G. C. Greubel, Oct 21 2021

Crossrefs

Cf. A009947, A117908.

Sequence in context: A352835 A349953 A349339 * A261094 A091538 A340991

Adjacent sequences: A117906 A117907 A117908 * A117910 A117911 A117912

Keyword

easy,nonn

Author

Paul Barry, Apr 01 2006

Status

approved