A279554 Number of length n inversion sequences avoiding the patterns 010, 101, 120, 201, and 210.

1, 1, 2, 5, 15, 51, 188, 733, 2979, 12495, 53708, 235396, 1048168, 4728757, 21569339, 99309057, 460932778, 2154402107

Offset: 0

Author

Megan A. Martinez, Dec 15 2016

Keywords

• nonn
• more

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 e_j <> e_k and e_i >= e_k. This is the same as the set of length n inversion sequences avoiding 010, 101, 120, 201, and 210.

Examples

			The length 3 inversion sequences are 000, 001, 002, 011, 012.
The length 4 inversion sequences are 0000, 0001, 0002, 0003, 0011, 0012, 0013, 0021, 0022, 0023, 0111, 0112, 0113, 0122, 0123.
		

Links

• Megan A. Martinez, Carla D. Savage, Patterns in Inversion Sequences II: Inversion Sequences Avoiding Triples of Relations, arXiv:1609.08106 [math.CO], 2016-2018.

Crossrefs

Cf. A263777, A263778, A263779, A263780, A279551, A279552, A279553, A279555, A279556, A279557, A279558, A279559, A279560, A279561, A279562, A279563, A279564, A279565, A279566, A279567, A279568, A279569, A279570, A279571, A279572, A279573.

Extensions

a(10)-a(11) from Alois P. Heinz, Feb 24 2017

a(12)-a(17) from Bert Dobbelaere, Dec 30 2018