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%I #4 Mar 30 2012 16:50:18
%S 1,1,1,1,1,1,1,2,2,1,1,2,2,2,1,1,2,4,4,2,1
%N Triangle read by rows: T(n,k) = number of inequivalent binary sequences of length n and weight k, where two sequences are said to be equivalent if they have the same set of phrases in their Ziv-Lempel encodings (the phrases can appear in a different order in the two sequences).
%C The Ziv-Lempel encoding scans the sequence from left to right and inserts a comma when the current phrase is an extension by one bit of an earlier phrase. In any case the scan ends with a comma. The phrases are the segments between the commas.
%C Equivalent sequences necessarily have the same Hamming weight.
%C See A106182 for further references and links.
%D J. Ziv and A. Lempel, A universal algorithm for sequential data compression. IEEE Trans. Information Theory IT-23 (1977), 337-343.
%e 1; 1,1; 1,1,1; 1,2,2,1; 1,2,2,2,1; 1,2,4,4,2,1; ... See A106182 for detailed examples.
%Y Row sums give A106182.
%K nonn,more,tabl
%O 1,8
%A _N. J. A. Sloane_, Aug 24 2005
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