OFFSET
0,3
COMMENTS
EXAMPLE
The partition y = (6,2,1,1) has multiplicities (1,1,2), which are biquanimous because we have the partition ((1,1),(2)), so y is not counted under a(10).
The a(1) = 1 through a(8) = 16 partitions:
(1) (2) (3) (4) (5) (6) (7) (8)
(11) (111) (22) (221) (33) (322) (44)
(211) (311) (222) (331) (332)
(1111) (2111) (321) (421) (422)
(11111) (411) (511) (431)
(3111) (2221) (521)
(21111) (4111) (611)
(111111) (22111) (2222)
(31111) (5111)
(211111) (22211)
(1111111) (32111)
(41111)
(221111)
(311111)
(2111111)
(11111111)
MATHEMATICA
biqQ[y_]:=MemberQ[Total/@Subsets[y], Total[y]/2];
Table[Length[Select[IntegerPartitions[n], !biqQ[Length/@Split[#]]&]], {n, 0, 30}]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Apr 18 2024
STATUS
approved