A120910
identification: the entry's rule defines the sequence for every index; tail: the sequence is the entry's tail after some prefix rows; match_*: finite agreement only.
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A120910: Triangle read by rows: T(n,k) is the number of ternary words of length n having k levels (n >= 1, 0 <= k <= n-1). A level is a pair of identical consecutive letters.
(identification, match triangle)
3 · 6, 3 · 12, 12, 3 · 24, 36, 18, 3 … row sums 3, 9, 27, 81, 243, 729, 2187, 6561, …
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A120909: Triangle read by rows: T(n,k) is the number of ternary words of length n having k runs (i.e., subwords of maximal length) of identical letters (1 <= k <= n).
(match reversed triangle)
3 · 3, 6 · 3, 12, 12 · 3, 18, 36, 24 … row sums 3, 9, 27, 81, 243, 729, 2187, 6561, …