A279552 Number of length n inversion sequences avoiding the patterns 000 and 010.

1, 1, 2, 4, 10, 29, 95, 345, 1376, 5966, 27886, 139608, 744552, 4210191, 25140790, 157981820, 1041480482, 7183374125, 51711299169, 387683162541, 3020997261596, 24424884853963, 204559337781097, 1772011400733378, 15855597322378302, 146360032952969570

Offset: 0

Author

Megan A. Martinez, Dec 15 2016

Keywords

• nonn

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 000 and 010.

Examples

			For n=3, the inversion sequences are 001, 002, 011, 012.
For n=4, the inversion sequences are 0011, 0012, 0013, 0021, 0022, 0023, 0112, 0113, 0122, 0123.
		

Links

• Benjamin Testart, Table of n, a(n) for n = 0..200
• Megan A. Martinez and Carla D. Savage, Patterns in Inversion Sequences II: Inversion Sequences Avoiding Triples of Relations, arXiv:1609.08106 [math.CO], 2016.
• Benjamin Testart, Inversion sequences avoiding the pattern 010, arXiv:2212.07222 [math.CO], 2022.
• Benjamin Testart, Completing the enumeration of inversion sequences avoiding one or two patterns of length 3, arXiv:2407.07701 [math.CO], 2024.

Crossrefs

Cf. A263777, A263778, A263779, A263780, A279551, A279553, A279554, A279555, A279556, A279557, A279558, A279559, A279560, A279561, A279562, A279563, A279564, A279565, A279566, A279567, A279568, A279569, A279570, A279571, A279572, A279573.

Extensions

a(10)-a(20) from Alois P. Heinz, Feb 23 2017

a(21) onwards from Benjamin Testart, Feb 01 2023