A258281 Number of partitions of 3 copies of n into distinct parts.

1, 1, 4, 5, 13, 18, 37, 56, 103, 154, 279, 398, 682, 1027, 1664, 2433, 3977, 5755, 8957, 13173, 19980, 29002, 43894, 62562, 92531, 133550, 193348, 274049, 398218, 558839, 796906, 1120833, 1577874, 2197279, 3089063, 4258348, 5915878, 8170572, 11231601, 15355764

Offset: 5

Author

Alois P. Heinz, May 25 2015

Keywords

• nonn

Examples

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

Links

• Alois P. Heinz, Table of n, a(n) for n = 5..200

Crossrefs

Column k=3 of A258280.

Programs

Mathematica

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 *)

Formula

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