A034163 Number of partitions of n into 3 distinct parts from [ 1,20 ].

0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 4, 5, 7, 8, 10, 12, 14, 16, 19, 21, 24, 27, 30, 33, 36, 38, 40, 42, 43, 44, 45, 45, 45, 45, 44, 43, 42, 40, 38, 36, 33, 30, 27, 24, 21, 19, 16, 14, 12, 10, 8, 7, 5, 4, 3, 2, 1, 1, 0, 0, 0, 0, 0, 0

Offset

0,9

Links

Table of n, a(n) for n=0..63.

Formula

Coefficient of t^3 in (1+tx)(1+tx^2)(1+tx^3)...(1+tx^20).

Mathematica

Table[Count[IntegerPartitions[n, {3}], _?(Length[Union[#]]==3&&Max[#]<21&)], {n, 0, 70}] (* Harvey P. Dale, Jul 31 2022 *)

Crossrefs

Sequence in context: A034160 A034161 A034162 * A242678 A034092 A211540

Adjacent sequences: A034160 A034161 A034162 * A034164 A034165 A034166

Keyword

nonn

Author

N. J. A. Sloane.

Status

approved