A182473 Number of partitions of n into exactly 2 different parts with distinct multiplicities.

0, 0, 0, 0, 1, 3, 3, 8, 9, 12, 16, 22, 20, 31, 35, 34, 44, 51, 53, 62, 65, 68, 87, 86, 89, 95, 118, 108, 126, 127, 138, 142, 162, 154, 188, 160, 193, 189, 227, 204, 228, 221, 258, 238, 282, 247, 311, 272, 320, 284, 344, 318, 373, 327, 398, 334, 407, 380, 450

Offset

0,6

Links

Alois P. Heinz, Table of n, a(n) for n = 0..3000

Example

a(4) = 1: [2,1,1], part 2 occurs once and part 1 occurs twice.
a(5) = 3: [2,1,1,1], [2,2,1], [3,1,1].
a(6) = 3: [2,1,1,1,1], [3,1,1,1], [4,1,1].
a(7) = 8: [2,1,1,1,1,1], [2,2,1,1,1], [2,2,2,1], [3,1,1,1,1], [3,2,2], [3,3,1], [4,1,1,1], [5,1,1].

Mathematica

dp2Q[n_]:=With[{sp=Split[n]}, Length[sp]==2&&Length[sp[[1]]]!=Length[sp[[2]]]]; Table[Length[Select[IntegerPartitions[k], dp2Q]], {k, 0, 60}] (* Harvey P. Dale, Dec 24 2025 *)

Crossrefs

Column k=2 of A182485.

Cf. A242900 (the same for compositions).

Sequence in context: A231855 A368738 A135477 * A383111 A363125 A335602

Adjacent sequences: A182470 A182471 A182472 * A182474 A182475 A182476

Keyword

nonn,look

Author

Alois P. Heinz, Apr 30 2012

Status

approved