OFFSET
0,3
EXAMPLE
The a(0) = 1 through a(7) = 14 partitions:
() (1) (2) (3) (4) (5) (6) (7)
(11) (21) (22) (32) (33) (43)
(111) (31) (41) (42) (52)
(211) (221) (51) (61)
(1111) (311) (222) (322)
(2111) (321) (331)
(11111) (411) (421)
(2211) (511)
(3111) (2221)
(21111) (4111)
(111111) (22111)
(31111)
(211111)
(1111111)
For example, the partition (4,3,3,3,2,2,2,1) has multiplicities (1,3,3,1), and since both multiplicities 1 and 3 appear twice, (4,3,3,3,2,2,2,1) is counted under a(20).
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], SameQ@@Length/@Split[Sort[Length/@Split[#]]]&]], {n, 0, 30}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 01 2019
STATUS
approved