A279556 Number of length n inversion sequences avoiding the patterns 010, 110, and 120.

1, 1, 2, 5, 15, 51, 190, 759, 3206, 14180, 65203, 309998, 1517330, 7619541, 39145113, 205261890, 1096393056, 5955598301, 32852080738, 183797522935, 1041802426740, 5977047039743, 34679912608313, 203345277644481, 1204104271508239, 7196256426157901

Offset: 0

Author

Megan A. Martinez, Dec 16 2016

Keywords

• nonn
• changed

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_k and e_i >= e_k. This is the same as the set of length n inversion sequences avoiding 010, 110, and 120.

Examples

			The length 3 inversion sequences avoiding (010, 110, 120) are 000, 001, 002, 011, 012
The length 4 inversion sequences avoiding (010, 110, 120) are 0000, 0001, 0002, 0003, 0011, 0012, 0013, 0021, 0022, 0023, 0111, 0112, 0113, 0122, 0123.
		

Links

• Nicholas R. Beaton, Table of n, a(n) for n = 0..54
• Megan A. Martinez and 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, A279554, A279555, 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(16) from Bert Dobbelaere, Dec 30 2018

a(17)-a(25) from Nicholas R. Beaton, Aug 29 2025