A279562 Number of length n inversion sequences avoiding the patterns 100, 102, and 201.

1, 1, 2, 6, 21, 78, 299, 1176, 4729, 19378, 80667, 340260, 1451277, 6248758, 27124703, 118576648, 521574769, 2306766426, 10251761219, 45759404076, 205050758165, 922104978430, 4160045001703, 18823187479504, 85400356099001, 388422301113250, 1770695668597643, 8089198184655732, 37027394471695197

Offset: 0

Author

Megan A. Martinez, Feb 09 2017

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_j <= e_k and e_i <> e_k. This is the same as the set of length n inversion sequences avoiding 100, 102, and 201.

Examples

			The length 4 inversion sequences avoiding (100, 102, 201) are 0000, 0001, 0002, 0003, 0010, 0011, 0012, 0013, 0020, 0021, 0022, 0023, 0101, 0110, 0111, 0112, 0113, 0120, 0121, 0122, 0123.
		

Links

• Nathan J. Britt, Table of n, a(n) for n = 0..1000
• 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. A000108, A057552, A263777, A263778, A263779, A263780, A279551, A279552, A279553, A279554, A279555, A279556, A279557, A279558, A279559, A279560, A279561, A279563, A279564, A279565, A279566, A279567, A279568, A279569, A279570, A279571, A279572, A279573.

Formula

G.f.: (2 + x - 10*x^2 + 4*x^3 - (2-3*x)*(1 - 4*x - 4*x^2)^(1/2)) / (8*x*(1 - x)^2). - Nathan J. Britt, Jun 08 2025

a(n) ~ c * (2 + 2*sqrt(2))^n / n^(3/2), where c = 0.40413545332026258682681691461076303199449216224437... - Nathan J. Britt, Jun 08 2025

Extensions

a(10)-a(12) from Alois P. Heinz, Feb 24 2017

a(13)-a(17) from Bert Dobbelaere, Dec 30 2018

More terms from Nathan J. Britt, Jun 08 2025