A089643 - OEIS

%I #31 Apr 24 2021 08:51:46

%S 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,

%T 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,

%U 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

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

%H Antti Karttunen, <a href="/A089643/b089643.txt">Table of n, a(n) for n = 0..19683</a>

%F a(n) = A007949(A005809(n)). - _Antti Karttunen_, Jul 29 2017

%F a(n) = A054861(3*n) - A054861(2*n) - A054861(n). - _David A. Corneth_, Jul 29 2017

%F a(n) = A053735(2*n)/2. - _Amiram Eldar_, Feb 21 2021

%t Table[IntegerExponent[Binomial[3 n, n], 3], {n, 0, 104}] (* _Michael De Vlieger_, Jul 29 2017 *)

%o (PARI) a(n)=valuation(binomial(3*n,n),3)

%o (Python)

%o from sympy import binomial

%o def a007949(n): return 0 if n%3 else a007949(n//3) + 1

%o def a(n): return a007949(binomial(3*n, n))

%o print([a(n) for n in range(151)]) # _Indranil Ghosh_, Jul 29 2017

%Y Cf. A005809, A007949, A053735, A054861.

%K nonn,easy

%O 0,5

%A _Benoit Cloitre_, Jan 01 2004