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A spider graph, spider tree, or simply "spider," is a tree with one vertex of degree at least 3 and all others with degree at most 2. The numbers of spiders on n=1, 2, ... nodes are 0, 0, 0, 1, 2, 4, 7, 11, 17, 25, 36, 50, 70, 94, ... (OEIS A004250). The count s_n of spider trees with n nodes is the same as the number of integer partitions of n-1 into three or more parts. It also has closed form s_n=P(n-1)-|_(n+1)/2_|, (1) where P(n) is the partition function P and |_z_| is...