A363745 Number of integer partitions of n whose rounded-down mean is 2.

0, 0, 1, 0, 2, 2, 3, 4, 10, 6, 16, 21, 24, 32, 58, 47, 85, 111, 119, 158, 248, 217, 341, 442, 461, 596, 867, 792, 1151, 1465, 1506, 1916, 2652, 2477, 3423, 4298, 4381, 5488, 7334, 6956, 9280, 11503, 11663, 14429, 18781, 17992, 23383, 28675, 28970, 35449, 45203

Offset: 0

Author

Gus Wiseman, Jul 05 2023

Keywords

• nonn

Examples

			The a(2) = 1 through a(10) = 16 partitions:
  (2)  .  (22)  (32)  (222)  (322)  (332)   (3222)  (3322)
          (31)  (41)  (321)  (331)  (422)   (3321)  (3331)
                      (411)  (421)  (431)   (4221)  (4222)
                             (511)  (521)   (4311)  (4321)
                                    (611)   (5211)  (4411)
                                    (2222)  (6111)  (5221)
                                    (3221)          (5311)
                                    (3311)          (6211)
                                    (4211)          (7111)
                                    (5111)          (22222)
                                                    (32221)
                                                    (33211)
                                                    (42211)
                                                    (43111)
                                                    (52111)
                                                    (61111)
		

Crossrefs

For 1 instead of 2 we have A025065, ranks A363949.

The high version is A026905 reduplicated, ranks A363950.

Column k = 2 of A363945.

These partitions have ranks A363954.

A008284 counts partitions by length, A058398 by mean.

A051293 counts subsets with integer mean, median A000975.

A067538 counts partitions with integer mean, strict A102627, ranks A316413.

A349156 counts partitions with non-integer mean, ranks A348551.

Cf. A000041, A002865, A027336, A237984, A241131, A327472, A327482, A363723, A363943, A363944, A363946.

Programs

Mathematica

Table[Length[Select[IntegerPartitions[n],Floor[Mean[#]]==2&]],{n,0,30}]