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A117909
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Count, inserting 0 after every even number.
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2
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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
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0,2
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COMMENTS
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Row sums of A117908.
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LINKS
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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)
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FORMULA
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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
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MATHEMATICA
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Riffle[Range[60], 0, 3] (* Harvey P. Dale, Sep 12 2013 *)
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PROG
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(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
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CROSSREFS
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Cf. A009947, A117908.
Sequence in context: A352835 A349953 A349339 * A261094 A091538 A340991
Adjacent sequences: A117906 A117907 A117908 * A117910 A117911 A117912
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry, Apr 01 2006
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STATUS
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approved
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