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  "body": "\n## Summary\n\nThe Motzkin number $M_n$ counts certain [[lattice paths|040WY0TT2G]] from $(0, 0)$ to $(n, 0)$, see the [[definition|PHA1S6GQGV]].\nThe paths use up, down and flat steps and never go below the horizontal axis.\nIt also counts the ways to draw non-crossing chords between $n$ points on a circle.\nThe sequence starts $1, 1, 2, 4, 9, 21, 51, 127$.\nThe Motzkin numbers are a close relative of the [[Catalan numbers|0YWZJEABB2]], which count the same paths without flat steps.\n\n## Explanations\n\n### L1 human\n\nImagine a walker who takes $n$ steps to the right, and each step goes up, down or stays level.\nThe walker starts and ends at height $0$ and never goes underground.\nFor $n = 3$ the possible walks are level-level-level, up-down-level, level-up-down and up-level-down.\nSo $M_3 = 4$.\n",
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