A244252 Total number of incoming edges at depth n in the solid partitions graph.

1, 4, 16, 46, 128, 332, 842, 2042, 4846, 11146, 25114, 55310, 119662, 254354, 532784, 1100411, 2245118, 4528212, 9038898, 17868025, 35006932, 68008606, 131083778, 250774482, 476372848, 898837825, 1685107392, 3139812791, 5816015908, 10712596279, 19625001436, 35765137033, 64853219808, 117031972499, 210211082354, 375886565558, 669232663688, 1186538314110, 2095236499224, 3685445929502

Offset

1,2

Comments

The solid partition graph is constructed as a directed graph whose vertices are solid partitions. The root vertex of the graph is the unique solid partition with one node. Given a solid partition, draw on outward directed edge to all solid partitions that can be obtained by the addition of a single node to the solid partition. The depth of a given vertex is given by the number of its nodes.

Links

Table of n, a(n) for n=1..40.

N. Destainville and S. Govindarajan, Estimating the asymptotics of solid partitions, arXiv:1406.5605 [cond-mat.stat-mech], 2014.

Example

a(2) = 4 as all four solid partitions of 2 are connected to the root vertex.

Crossrefs

Cf. A000293, A090984, A000070.

Sequence in context: A055342 A213292 A174836 * A369401 A308592 A050616

Adjacent sequences: A244249 A244250 A244251 * A244253 A244254 A244255

Keyword

nonn,hard

Author

Suresh Govindarajan, Jun 23 2014

Status

approved