Motzkin numbers. Number of rooted planar unlabeled unary-binary trees with N nodes. Use this tag when calculating Motzkin numbers, e.g. 1, 1, 2, 4, 9, 21, 51, 127, or with enumerating unary-binary trees, or binary expression trees, or related combinatorics . Note: Don't confuse binary expression trees with strictly binary trees used with expressions, binary expression trees have unary edges.
Motzkin numbers. Number of rooted planar unlabeled unary-binary trees with N nodes.
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Related sequences
Motzkin numbers are for regular binary trees, e.g. all nodes have 0,1, or 2 branches, and count all nodes, while Catalan numbers are for full binary trees, e.g. all nodes have 0 or 2 branches, and count only leaves, while
