Unrooted binary tree enumeration problem on unrooted binary trees is to count the number of trees with "n" labeled leaves and unlabeled internal nodes. An unrooted binary tree on "n" labeled leaves can be formed by connecting the "n"th leaf to a new node in the middle of any of the edges of an unrooted binary tree on "n" − 1 labeled leaves. There are 2"n" − 5 edges at which the "n"th node can be attached; therefore, the number of trees on "n" leaves is larger than the number of trees on "n" − 1 leaves by a factor of 2"n" −
Binary system a binary system but are not. Such objects merely appear to be close together, but lie at different distances from the solar system. When binary minor planets are similar in size, they may be called "binary companions" instead of referring to the smaller body as a satellite. Good examples of true binary companions are the 90 Antiope and the 79360 Sila–Nunam systems. Pluto and its largest moon Charon are sometimes described as a binary system because the barycenter (center of mass) of the two objects is not inside either of them. Binary system A binary system is a system of