|
|
A279555
|
|
Number of length n inversion sequences avoiding the patterns 110, 210, 120, and 010.
|
|
23
|
|
|
1, 1, 2, 5, 15, 51, 189, 746, 3091, 13311, 59146, 269701, 1256820, 5966001, 28773252, 140695923, 696332678, 3483193924, 17589239130, 89575160517, 459648885327, 2374883298183, 12346911196912, 64555427595970, 339276669116222, 1791578092326881, 9501960180835998
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
COMMENTS
|
A length n inversion sequence e_1e_2...e_n is a sequence of integers where 0 <= e_i <= i-1. The term a(n) counts those length n inversion sequences with no entries e_i, e_j, e_k (where i<j<k) such that e_j > e_k and e_i >= e_k. This is the same as the set of length n inversion sequences avoiding 010, 110, 120, and 210.
It can be shown that this sequence also counts the length n inversion sequences with no entries e_i, e_j, e_k (where i<j<k) such that e_i <> e_j >=e_k and e_i >= e_k. This is the same as the set of length n inversion sequences avoiding 010, 100, 120, and 210.
|
|
LINKS
|
|
|
EXAMPLE
|
The length 3 inversion sequences avoiding (010, 110, 120, 210) are 000, 001, 002, 011, 012.
The length 4 inversion sequences avoiding (010, 110, 120, 210) are 0000, 0001, 0002, 0003, 0011, 0012, 0013, 0021, 0022, 0023, 0111, 0112, 0113, 0122, 0123.
|
|
CROSSREFS
|
Cf. A263777, A263778, A263779, A263780, A279551, A279552, A279553, A279554, A279556, A279557, A279558, A279559, A279560, A279561, A279562, A279563, A279564, A279565, A279566, A279567, A279568, A279569, A279570, A279571, A279572, A279573.
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|