A130123
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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A130123: Infinite lower triangular matrix with 2^k in the right diagonal and the rest zeros. Triangle, T(n,k), n zeros followed by the term 2^k. Triangle by columns, (2^k, 0, 0, 0, ...).
(identification, match triangle)
1 · 0, 2 · 0, 0, 4 · 0, 0, 0, 8 … row sums 1, 2, 4, 8, 16, 32, 64, 128, …