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

Author

Suresh Govindarajan, Jun 23 2014

Keywords

• nonn
• hard

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.

Examples

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

Links

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

Crossrefs

Cf. A000293, A090984, A000070.