bibkey: meeussen2025a381265 authors: Wouter Meeussen year: 2025 title: “OEIS A381265, solid partitions with two layers and second layer a plane partition of 3: formula conjecture” doi: null url: https://oeis.org/A381265 claim: “The entry counts the solid (3D) partitions with two layers whose second layer is a plane partition of 3 (data a(3) = 6, 21, 57, …) and records the conjecture that the count equals 3*(2A000219 - A000990 - 2A000041 + 1), tested up to n = 20.” strata_touched:

• D5/S3/Combinatorics/TwoLayerSolidPartitions license: citation-only triage: anchor

OEIS A381265

A381265 (Wouter Meeussen, 2025-02-18, offset 3, data 6, 21, 57, 138, 294, 606, …) is

a(n) is the number of solid (3D) partitions of n with 2 layers and second layer a plane partition of 3.

with the COMMENTS line

Conjecture: equal to 3*(2A000219 -A000990 -2A000041 +1) tested up to n=20.

and a conjectured generating function in the formula field. Its EXAMPLE lists the six solid partitions for a(3) = 6, each with two layers of 3 cells, so the index is the size of the first layer. A000219, A000990 and A000041 count the plane partitions, the plane partitions with at most two rows and the partitions of n.

Verified locator

• URL: https://oeis.org/A381265 (revision 8, last modified 2025-02-18, name, comment, formula and example fields; retrieved 2026-09-27 through the OEIS JSON interface).