OFFSET
0,3
COMMENTS
Numerator of n/3. - Wesley Ivan Hurt, Jul 18 2014
LINKS
Reinhard Zumkeller, 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
a(n) = n / gcd(n,3).
G.f.: x*(1+2*x+x^2+2*x^3+x^4)/(1-x^3)^2 = x*(1+2*x+x^2+2*x^3+x^4) / ( (x-1)^2*(1+x+x^2)^2 ). - Len Smiley, Apr 30 2001
Multiplicative with a(3^e) = 3^(e-1), a(p^e) = p^e otherwise. - Mitch Harris, Jun 09 2005
a(n) = A167192(n+3, 3). - Reinhard Zumkeller, Oct 30 2009
From R. J. Mathar, Apr 18 2011: (Start)
a(n) = A109044(n)/3.
Dirichlet g.f.: zeta(s-1)*(1-2/3^s). (End)
G.f.: x /(1 - x)^2 - 2 * x^3/(1 - x^3)^2. - Michael Somos, Mar 05 2017
a(n) = a(-n) for all n in Z. - Michael Somos, Mar 05 2017
a(n) = n*(7 - 4*cos((2*Pi*n)/3)) / 9. - Colin Barker, Mar 05 2017
Sum_{k=1..n} a(k) ~ (7/18) * n^2. - Amiram Eldar, Nov 25 2022
Sum_{n>=1} (-1)^(n+1)/a(n) = 5*log(2)/3. - Amiram Eldar, Sep 08 2023
EXAMPLE
G.f. = x + 2*x^2 + x^3 + 4*x^4 + 5*x^5 + 2*x^6 + 7*x^7 + 8*x^8 + 3*x^9 + ...
MAPLE
MATHEMATICA
If[Divisible[#, 3], #/3, #]&/@Range[0, 70] (* Harvey P. Dale, Feb 07 2011 *)
a[n_] := Numerator[n/3]; Array[a, 100, 0] (* Wesley Ivan Hurt, Jul 18 2014 *)
PROG
(Haskell)
a051176 n = if m == 0 then n' else n where (n', m) = divMod n 3
-- Reinhard Zumkeller, Aug 27 2012
(PARI) a(n) = if (n % 3, n, n/3); \\ Michel Marcus, Feb 02 2016
(Magma) [Numerator(n/3): n in [0..70]]; // G. C. Greubel, Feb 19 2019
(Sage) [numerator(n/3) for n in range(70)] # G. C. Greubel, Feb 19 2019
CROSSREFS
KEYWORD
nonn,easy,mult
AUTHOR
STATUS
approved