%I #11 Apr 07 2017 10:29:24

%S 1,1,4,5,13,18,37,56,103,154,279,398,682,1027,1664,2433,3977,5755,

%T 8957,13173,19980,29002,43894,62562,92531,133550,193348,274049,398218,

%U 558839,796906,1120833,1577874,2197279,3089063,4258348,5915878,8170572,11231601,15355764

%N Number of partitions of 3 copies of n into distinct parts.

%H Alois P. Heinz, <a href="/A258281/b258281.txt">Table of n, a(n) for n = 5..200</a>

%F a(n) = 1/6 * [(x*y*z)^n] Product_{j>0} (1+x^j+y^j+z^j).

%e a(7) = 4: [7;6,1;5,2], [7;6,1;4,3], [7;5,2;4,3], [6,1;5,2;4,3].

%t nmax = 30; p = 1; Do[p = Expand[p*(1 + x^j + y^j + z^j)]; p = Select[p, (Exponent[#, x] <= nmax) && (Exponent[#, y] <= nmax) && (Exponent[#, z] <= nmax) &], {j, 1, nmax}]; p = Select[p, Exponent[#, x] == Exponent[#, y] == Exponent[#, z] &]; Table[Coefficient[p, x^n*y^n*z^n]/6, {n, 5, nmax}] (* _Vaclav Kotesovec_, Apr 07 2017 *)

%Y Column k=3 of A258280.

%K nonn

%O 5,3

%A _Alois P. Heinz_, May 25 2015