OFFSET
0,5
EXAMPLE
The a(9) = 4 through a(14) = 15 compositions (A..E = 10..14):
(9) (A) (B) (C) (D) (E)
(333) (2233) (141122) (2244) (161122) (2255)
(121122) (3322) (221123) (4422) (221125) (5522)
(221121) (131122) (221132) (151122) (221134) (171122)
(221131) (221141) (221124) (221143) (221126)
(231122) (221142) (221152) (221135)
(321122) (221151) (221161) (221153)
(241122) (251122) (221162)
(421122) (341122) (221171)
(431122) (261122)
(521122) (351122)
(531122)
(621122)
(122121122)
(221121221)
MATHEMATICA
yosQ[y_]:=Length[y]<=1||MemberQ[Subsets[y], Length/@Split[y]]&&yosQ[Length/@Split[y]];
Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], yosQ]], {n, 0, 15}]
CROSSREFS
The non-recursive reverse version is A353403.
The consecutive version is A353430.
These compositions are ranked by A353431.
A011782 counts compositions.
A114901 counts compositions with no runs of length 1.
A325705 counts partitions containing all of their distinct multiplicities.
A329739 counts compositions with all distinct run-length.
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, May 15 2022
STATUS
approved