A352882 a(n) is the number of plane corner cuts of size n.

1, 1, 2, 3, 4, 6, 7, 8, 10, 12, 13, 16, 16, 18, 20, 23, 24, 26, 26, 30, 32, 35, 34, 38, 38, 42, 44, 46, 47, 54, 52, 54, 52, 56, 60, 66, 67, 68, 66, 72, 72, 80, 74, 82, 84, 87, 86, 90, 88, 96, 96, 102, 96, 104, 104, 115, 114, 116, 110, 118, 114, 124, 122, 126, 134, 140, 135, 134, 132, 146, 144, 156, 144, 150, 152, 158

Offset

0,3

Comments

In Bergeron and Mazin, a(n) is the number of triangular partitions of size n.

Links

Alejandro B. Galván, Table of n, a(n) for n = 0..10000

François Bergeron and Mikhail Mazin, Combinatorics of Triangular Partitions, arXiv:2203.15942 [math.CO], (2022). See p. 2.

Sylvie Corteel, Gäel Rémond, Gilles Schaeffer, and Hugh Thomas, The Number of Plane Corner Cuts, Adv. in Appl. Math. 23, no. 1, (1999).

Sergi Elizalde and Alejandro B. Galván, Triangular partitions: enumeration, structure, and generation, arXiv:2312.16353 [math.CO], (2023).

Sergi Elizalde and Alejandro B. Galván, Combinatorial properties of triangular partitions, Proceedings of the 36th Conference on Formal Power Series and Algebraic Combinatorics (Bochum), Séminaire Lotharingien de Combinatoire 91B (2024) Article #68, 12 pp.

Alejandro B. Galván, C++ program.

Formula

See the g.f. at page 2 in Corteel et al.

Crossrefs

Cf. A007294, A275518.

Sequence in context: A336824 A114149 A294652 * A320143 A062974 A329399

Adjacent sequences: A352879 A352880 A352881 * A352883 A352884 A352885

Keyword

nonn

Author

Stefano Spezia, Apr 07 2022

Extensions

More terms from Alejandro B. Galván, Dec 29 2023

Status

approved