A279566 Number of length n inversion sequences avoiding the patterns 102 and 201.

1, 1, 2, 6, 22, 87, 354, 1465, 6154, 26223, 113236, 494870, 2185700, 9743281, 43784838, 198156234, 902374498, 4131895035, 19012201080, 87864535600, 407664831856, 1898184887679, 8867042353912, 41543375724751, 195164372948152, 919138464708907, 4338701289961694, 20524046955770940

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_i > e_j < e_k and e_i <> e_k. This is the same as the set of length n inversion sequences avoiding 102 and 201.

Links

Benjamin Testart, Table of n, a(n) for n = 0..1400

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

Benjamin Testart, Completing the enumeration of inversion sequences avoiding one or two patterns of length 3, arXiv:2407.07701 [math.CO], 2024.

Chunyan Yan, Zhicong Lin, Inversion sequences avoiding pairs of patterns, arXiv:1912.03674 [math.CO], 2019.

Formula

G.f.: (-8*x^4 + 18*x^3 - 10*x^2 - 8*x + 4 + 2 * (2*x - 1) * (x^2 - 2*x + 2) * ((5*x - 1)*(x - 1))^(1/2)) / (4*x * (2*x - 1) * (x - 1) * (x - 2)^2). - Benjamin Testart, Jul 12 2024

a(n) ~ 41 * 5^(n + 3/2) / (648 * sqrt(Pi) * n^(3/2)). - Vaclav Kotesovec, Nov 21 2024

Example

The length 4 inversion sequences avoiding (102, 201) are 0000, 0001, 0002, 0003, 0010, 0011, 0012, 0013, 0020, 0021, 0022, 0023, 0100, 0101, 0110, 0111, 0112, 0113, 0120, 0121, 0122, 0123

Crossrefs

Cf. A000108, A057552, A263777, A263778, A263779, A263780, A279551, A279552, A279553, A279554, A279555, A279556, A279557, A279558, A279559, A279560, A279561, A279562, A279563, A279564, A279565, A279567, A279568, A279569, A279570, A279571, A279572, A279573.

Sequence in context: A165532 A165533 A164651 * A367413 A150261 A308409

Adjacent sequences: A279563 A279564 A279565 * A279567 A279568 A279569

Keyword

nonn,changed

Author

Megan A. Martinez, Feb 09 2017

Extensions

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

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

a(18) and beyond from Benjamin Testart, Jul 12 2024

Status

approved