OFFSET
0,3
COMMENTS
A sequence is recursively strong if either it is empty or equal to (1), or its run-lengths are weakly decreasing (strong) and are themselves a recursively strong sequence.
A composition of n is a finite sequence of positive integers with sum n.
Also the number of recursively co-strong compositions of n.
EXAMPLE
The a(1) = 1 through a(5) = 11 compositions:
(1) (2) (3) (4) (5)
(11) (12) (13) (14)
(21) (22) (23)
(111) (31) (32)
(121) (41)
(211) (122)
(1111) (131)
(212)
(311)
(2111)
(11111)
MATHEMATICA
tni[q_]:=Or[q=={}, q=={1}, And[GreaterEqual@@Length/@Split[q], tni[Length/@Split[q]]]];
Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], tni]], {n, 0, 15}]
CROSSREFS
The total version is A316496.
The case of partitions is (also) A316496.
The co-strong case is A332274 (this sequence).
The case of reversed partitions is A332275.
The alternating version is A332338.
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Feb 11 2020
STATUS
editing