A383770 -id:A383770 - cp's OEIS frontend

A382361 Number of nonnesting permutations of the multiset {1,1,2,2,...,n,n} that avoid 123.

1, 4, 17, 82, 406, 2070, 10729, 56394, 299646, 1606816, 8683562

Offset: 1

Amya Luo, May 26 2025

Nonnesting permutations of the multiset {1,1,2,2,...,n,n} such that if abcd is a subsequence, then a=d implies b!=c. A permutation avoids 123 if it does not contain any subsequence abc such that a

Robert Dougherty-Bliss, Python program, May 28 2025.
Sergi Elizalde and Amya Luo, Pattern avoidance in nonnesting permutations, arXiv:2412.00336 [math.CO], 2024.
Sean A. Irvine, Java program (github)

Cf. A177555, A383770.

Python
```
# See Robert Dougherty-Bliss link
```

a(9)-a(11) from Sean A. Irvine, Jun 17 2025

A383771 Number of noncrossing permutations of [n] avoiding 213 (and by symmetry 132, 213, or 312).

Original entry on oeis.org

1, 1, 4, 19, 102, 590, 3588, 22617, 146460, 968520, 6513034, 44403604, 306209746, 2132165062, 14970030506, 105862919427, 753344866662, 5390772814578, 38765692377100, 279999861952626, 2030439981144348, 14776796428607224, 107891287190000212, 790105506941871258

Offset: 0

Robert P. Laudone, May 09 2025

nonn

K. Archer and R. P. Laudone, Pattern avoidance in non-crossing and non-nesting permutations, arXiv:2502.13309 [math.CO], 2025.

Cf. A383770.

G.f.: A(x) satisfies x^2*A(x)^4 - (x^2+x)*A(x)^3 - x*A(x)^2 + (x+1)*A(x) - 1 = 0.

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A382361 Number of nonnesting permutations of the multiset {1,1,2,2,...,n,n} that avoid 123.

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