A324516 - OEIS

%I #6 Mar 07 2019 23:25:05

%S 1,1,1,2,2,2,2,5,2,8,6,6,10,14,12,20,27,23,40,40,51,62,82,88,123,135,

%T 173,197,253,285,350,419,497,594,708,855,978,1195,1395,1648,1915,2313,

%U 2625,3170,3625,4336,4948,5900,6751,7970,9180,10704,12337,14436,16517

%N Number of integer partitions of n > 0 where the maximum part minus the minimum part equals the length minus the number of distinct parts.

%C The Heinz numbers of these integer partitions are given by A324515.

%e The a(8) = 5 through a(14) = 14 integer partitions:

%e   (8)      (9)      (A)       (B)       (C)        (D)        (E)

%e   (332)    (32211)  (433)     (443)     (4422)     (544)      (554)

%e   (3311)            (3331)    (33221)   (33321)    (43222)    (4442)

%e   (32111)           (4222)    (44111)   (422211)   (52222)    (5333)

%e   (41111)           (32221)   (422111)  (5211111)  (422221)   (43322)

%e                     (33211)   (431111)  (6111111)  (433111)   (44411)

%e                     (421111)                       (442111)   (442211)

%e                     (511111)                       (4321111)  (443111)

%e                                                    (5221111)  (551111)

%e                                                    (5311111)  (4322111)

%e                                                               (5222111)

%e                                                               (5411111)

%e                                                               (62111111)

%e                                                               (71111111)

%t Table[Length[Select[IntegerPartitions[n],Max@@#-Min@@#==Length[#]-Length[Union[#]]&]],{n,30}]

%Y Cf. A006141, A039900, A046660, A047993, A064174, A243055.

%Y Cf. A324515, A324518, A324520.

%K nonn

%O 1,4

%A _Gus Wiseman_, Mar 06 2019