A366774 -id:A366774 - cp's OEIS frontend

A366775 Number of 2-distant 4-noncrossing partitions of {1,...,n}.

1, 1, 2, 5, 15, 52, 203, 877, 4140, 21146, 115938, 677765, 4200011, 27446229, 188255890, 1349652560, 10075332564, 78052115894, 625568350179, 5173033558415, 44028767332852, 384857341649657

Offset: 0

Juan B. Gil, Nov 13 2023

a(n+1) is the binomial transform of A108305.

			There are 21147 partitions of 9 elements, but a(9)=21146 because the partition (1,6)(2,7)(3,8)(4,9)(5) has a 2-distant 4-crossing.

Juan B. Gil and Jordan O. Tirrell, A simple bijection for enhanced, classical, and 2-distant k-noncrossing partitions, Discrete Math. 343 (2020), no. 6, 111705, 5 pp.

Juan B. Gil and Jordan O. Tirrell, A simple bijection for enhanced, classical, and 2-distant k-noncrossing partitions, arXiv:1806.09065 [math.CO], 2018-2023.

Cf. A108305, A366774, A366776.

a(n+1) = Sum_{i=0..n} binomial(n,i)*A108305(i).

A366776 Number of 2-distant 5-noncrossing partitions of {1,...,n}.

Original entry on oeis.org

1, 1, 2, 5, 15, 52, 203, 877, 4140, 21147, 115975, 678569, 4213546, 27642948, 190866373, 1382340849, 10469739750, 82701857286, 679644668584, 5797647603036, 51228938289039, 467980667203765

Offset: 0

Juan B. Gil, Nov 13 2023

a(n+1) is the binomial transform of A192126.

			There are 678570 partitions of 11 elements, but a(11)=678569 because the partition (1,7)(2,8)(3,9)(4,10)(5,11)(6) has a 2-distant 5-crossing.

Juan B. Gil and Jordan O. Tirrell, A simple bijection for enhanced, classical, and 2-distant k-noncrossing partitions, Discrete Math. 343 (2020), no. 6, 111705, 5 pp.

Juan B. Gil and Jordan O. Tirrell, A simple bijection for enhanced, classical, and 2-distant k-noncrossing partitions, arXiv:1806.09065 [math.CO], 2018-2023.

Cf. A192126, A366774, A366775.

a(n+1) = Sum_{i=0..n} binomial(n,i)*A192126(i).

cp's OEIS Frontend

A366775 Number of 2-distant 4-noncrossing partitions of {1,...,n}.

Views

Author

Keywords

Comments

Examples

References

Links

Crossrefs

Formula