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A332274
Number of totally strong compositions of n.
5
1, 1, 2, 4, 7, 11, 22, 33, 56, 93, 162, 264, 454, 765, 1307, 2237, 3849, 6611, 11472, 19831, 34446, 59865, 104293, 181561, 316924
OFFSET
0,3
COMMENTS
A sequence is totally strong if either it is empty, equal to (1), or its run-lengths are weakly decreasing (strong) and are themselves a totally strong sequence.
A composition of n is a finite sequence of positive integers with sum n.
Also the number of totally 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 case of partitions is A316496.
The co-strong case is A332274 (this sequence).
The case of reversed partitions is A332275.
The alternating version is A332338.
Sequence in context: A018077 A114347 A293684 * A071250 A084992 A360886
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Feb 11 2020
STATUS
approved