A324469 Exponent of highest power of 3 that divides multinomial(4*n;n,n,n,n).

0, 1, 2, 1, 2, 4, 2, 5, 6, 1, 2, 3, 2, 3, 6, 4, 6, 7, 2, 3, 4, 5, 6, 8, 6, 8, 9, 1, 2, 3, 2, 3, 5, 3, 6, 7, 2, 3, 4, 3, 4, 8, 6, 8, 9, 4, 5, 6, 6, 7, 9, 7, 9, 10, 2, 3, 4, 3, 4, 6, 4, 9, 10, 5, 6, 7, 6, 7, 10, 8, 10, 11, 6, 7, 8, 8, 9, 11, 9, 11, 12, 1, 2

Offset: 0

Author

N. J. A. Sloane, Mar 03 2019

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 0..10000

Crossrefs

Analogs for binomial and trinomials: A000989, A053735. See also A324467.

Cf. A007949 (3-adic valuation of n), A008977.

Programs

Maple

[seq(padic[ordp](combinat[multinomial](4*n, n$4), 3), n=0..128)];

Mathematica

s[n_] := Plus @@ IntegerDigits[n, 3]; a[n_] := 2*s[n] - s[4*n]/2; Array[a, 100, 0] (* Amiram Eldar, Feb 21 2021 *)

Formula

a(n) = 2*A000989(n) + A000989(2*n). - Charlie Neder, Mar 09 2019

From Amiram Eldar, Feb 21 2021: (Start)

a(n) = A007949(A008977(n)).

a(n) = 2*A053735(n) - A053735(4*n)/2. (End)