Number of sequences with one word once, one word twice, and a third word once (and one unused) — but in 4 rolls, the frequency vector is (2,1,1,0).

Mon, 20 Apr 2026 03:55:51 +0000

Understanding Intriguing Word Pattern Sequences: One Word Once, One Twice, and One Unique Word (With a Silent Fourth Element) In the fascinating world of linguistic patterns and combinatorial sequences, researchers and language enthusiasts often explore structured word combinations that reveal hidden symmetries and constraints. One such intriguing pattern involves sequences constructed from four distinct words—where exactly one word appears once, one word appears twice, and a third word appears exactly once—while a fourth potential word remains unused (frequency zero). This configuration yields a unique frequency vector (2,1,1,0), pointing to a balanced yet asymmetric linguistic motif. ### The Frequency Pattern (2,1,1,0) Explained The frequency vector (2,1,1,0) represents:
- 2 occurrences: One word that repeats once (double usage)
- 1 occurrence: One word used exactly once
- 1 occurrence: A second distinct word used once
- 0 occurrence: A fourth word present in the full lexicon but absent here