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

0,5

Links

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

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A005809, A007949, A053735, A054861.

Sequence in context: A087974 A008679 A029435 * A360240 A185090 A115268

Adjacent sequences: A089640 A089641 A089642 * A089644 A089645 A089646

Keyword

nonn,easy

Author

Benoit Cloitre, Jan 01 2004

Status

approved