A332274 Number of totally strong compositions of n.

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.

Links

Table of n, a(n) for n=0..24.

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.

Cf. A100883, A107429, A317245, A317256, A317491, A329744, A332272, A332279, A332289, A332292, A332336, A332337, A332339, A332340.

Sequence in context: A018077 A114347 A293684 * A071250 A084992 A360886

Adjacent sequences: A332271 A332272 A332273 * A332275 A332276 A332277

Keyword

nonn,more

Author

Gus Wiseman, Feb 11 2020

Status

approved