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%I #17 Jun 26 2014 17:47:43
%S 1,4,16,46,128,332,842,2042,4846,11146,25114,55310,119662,254354,
%T 532784,1100411,2245118,4528212,9038898,17868025,35006932,68008606,
%U 131083778,250774482,476372848,898837825,1685107392,3139812791,5816015908,10712596279,19625001436,35765137033,64853219808,117031972499,210211082354,375886565558,669232663688,1186538314110,2095236499224,3685445929502
%N Total number of incoming edges at depth n in the solid partitions graph.
%C 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.
%H N. Destainville and S. Govindarajan, <a href="http://arxiv.org/abs/1406.5605">Estimating the asymptotics of solid partitions</a>, arXiv:1406.5605 [cond-mat.stat-mech], 2014.
%e a(2) = 4 as all four solid partitions of 2 are connected to the root vertex.
%Y Cf. A000293, A090984, A000070.
%K nonn,hard
%O 1,2
%A _Suresh Govindarajan_, Jun 23 2014