OFFSET
0,2
COMMENTS
A sequence is strictly recursively normal if either it empty, its run-lengths are distinct (strict), or its run-lengths cover an initial interval of positive integers (normal) and are themselves a strictly recursively normal sequence.
EXAMPLE
The a(1) = 1 through a(9) = 15 partitions:
(1) (2) (3) (4) (5) (6) (7) (8) (9)
(21) (31) (32) (42) (43) (53) (54)
(211) (41) (51) (52) (62) (63)
(221) (321) (61) (71) (72)
(311) (411) (322) (332) (81)
(331) (422) (432)
(421) (431) (441)
(511) (521) (522)
(3211) (611) (531)
(3221) (621)
(4211) (711)
(3321)
(4221)
(4311)
(5211)
(32211)
MATHEMATICA
normQ[m_]:=m=={}||Union[m]==Range[Max[m]];
recnQ[ptn_]:=With[{qtn=Length/@Split[ptn]}, Or[ptn=={}, UnsameQ@@qtn, And[normQ[qtn], recnQ[qtn]]]];
Table[Length[Select[IntegerPartitions[n], recnQ]], {n, 0, 30}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 09 2020
STATUS
approved