OFFSET
0,8
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..500
FORMULA
a(n > 0) = 2^(n - 1) - A102726(n).
EXAMPLE
The a(6) = 1 through a(8) = 14 compositions:
(1,2,3) (1,2,4) (1,2,5)
(1,1,2,3) (1,3,4)
(1,2,1,3) (1,1,2,4)
(1,2,3,1) (1,2,1,4)
(1,2,2,3)
(1,2,3,2)
(1,2,4,1)
(2,1,2,3)
(1,1,1,2,3)
(1,1,2,1,3)
(1,1,2,3,1)
(1,2,1,1,3)
(1,2,1,3,1)
(1,2,3,1,1)
MATHEMATICA
Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], MatchQ[#, {___, x_, ___, y_, ___, z_, ___}/; x<y<z]&]], {n, 0, 10}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 22 2020
EXTENSIONS
Terms a(21) and beyond from Andrew Howroyd, Dec 31 2020
STATUS
approved