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

%I A324469 #25 Feb 21 2021 04:09:04
%S A324469 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,
%T A324469 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,
%U A324469 7,10,8,10,11,6,7,8,8,9,11,9,11,12,1,2
%N A324469 Exponent of highest power of 3 that divides multinomial(4*n;n,n,n,n).
%H A324469 Amiram Eldar, <a href="/A324469/b324469.txt">Table of n, a(n) for n = 0..10000</a>
%F A324469 a(n) = 2*A000989(n) + A000989(2*n). - _Charlie Neder_, Mar 09 2019
%F A324469 From _Amiram Eldar_, Feb 21 2021: (Start)
%F A324469 a(n) = A007949(A008977(n)).
%F A324469 a(n) = 2*A053735(n) - A053735(4*n)/2. (End)
%p A324469 [seq(padic[ordp](combinat[multinomial](4*n, n$4), 3), n=0..128)];
%t A324469 s[n_] := Plus @@ IntegerDigits[n, 3]; a[n_] := 2*s[n] - s[4*n]/2; Array[a, 100, 0] (* _Amiram Eldar_, Feb 21 2021 *)
%Y A324469 Analogs for binomial and trinomials: A000989, A053735. See also A324467.
%Y A324469 Cf. A007949 (3-adic valuation of n), A008977.
%K A324469 nonn
%O A324469 0,3
%A A324469 _N. J. A. Sloane_, Mar 03 2019