A089643 3^a(n) divides C(3n,n); 3-adic valuation of A005809.

0, 1, 1, 1, 2, 1, 1, 2, 2, 1, 2, 2, 2, 3, 1, 1, 2, 2, 1, 2, 2, 2, 3, 2, 2, 3, 3, 1, 2, 2, 2, 3, 2, 2, 3, 3, 2, 3, 3, 3, 4, 1, 1, 2, 2, 1, 2, 2, 2, 3, 2, 2, 3, 3, 1, 2, 2, 2, 3, 2, 2, 3, 3, 2, 3, 3, 3, 4, 2, 2, 3, 3, 2, 3, 3, 3, 4, 3, 3, 4, 4, 1, 2, 2, 2, 3, 2, 2, 3, 3, 2, 3, 3, 3, 4, 2, 2, 3, 3, 2, 3, 3, 3, 4, 3

Offset: 0

Author

Benoit Cloitre, Jan 01 2004

Keywords

• nonn
• easy

Links

• Antti Karttunen, Table of n, a(n) for n = 0..19683

Crossrefs

Cf. A005809, A007949, A053735, A054861.

Programs

Mathematica

Table[IntegerExponent[Binomial[3 n, n], 3], {n, 0, 104}] (* Michael De Vlieger, Jul 29 2017 *)

PARI

a(n)=valuation(binomial(3*n,n),3)

Python

from sympy import binomial
def a007949(n): return 0 if n%3 else a007949(n//3) + 1
def a(n): return a007949(binomial(3*n, n))
print([a(n) for n in range(151)]) # Indranil Ghosh, Jul 29 2017

Formula

a(n) = A007949(A005809(n)). - Antti Karttunen, Jul 29 2017

a(n) = A054861(3*n) - A054861(2*n) - A054861(n). - David A. Corneth, Jul 29 2017

a(n) = A053735(2*n)/2. - Amiram Eldar, Feb 21 2021