%I #6 May 02 2019 08:53:18

%S 0,0,1,1,2,1,3,1,4,2,5,1,8,1,7,5,10,2,16,4,21,15,24,17,49,29,53,53,84,

%T 65,121,92,148,141,186,179,280,223,317,318,428,387,576,512,700,734,

%U 899,900,1260,1207,1551,1668,2041,2109,2748,2795,3463,3775,4446

%N Number of totally abnormal integer partitions of n.

%C A multiset is normal if its union is an initial interval of positive integers. A multiset is totally abnormal if it is not normal and either it is a singleton or its multiplicities form a totally abnormal multiset.

%C The Heinz numbers of these partitions are given by A325372.

%e The a(2) = 1 through a(12) = 8 totally abnormal partitions (A = 10, B = 11, C = 12):

%e (2) (3) (4) (5) (6) (7) (8) (9) (A) (B) (C)

%e (22) (33) (44) (333) (55) (66)

%e (222) (2222) (3322) (444)

%e (3311) (4411) (3333)

%e (22222) (4422)

%e (5511)

%e (222222)

%e (333111)

%t normQ[m_]:=Or[m=={},Union[m]==Range[Max[m]]];

%t antinrmQ[ptn_]:=!normQ[ptn]&&(Length[ptn]==1||antinrmQ[Sort[Length/@Split[ptn]]]);

%t Table[Length[Select[IntegerPartitions[n],antinrmQ]],{n,0,30}]

%Y Cf. A181819, A275870, A305563, A317088, A317245, A317491, A317589, A319149, A319810, A325372.

%K nonn

%O 0,5

%A _Gus Wiseman_, May 01 2019