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

5,3

Links

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

Formula

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

Example

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

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 *)

Crossrefs

Column k=3 of A258280.

Sequence in context: A091183 A372122 A234254 * A094029 A005672 A147001

Adjacent sequences: A258278 A258279 A258280 * A258282 A258283 A258284

Keyword

nonn

Author

Alois P. Heinz, May 25 2015

Status

approved