

A109338


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 ZivLempel encodings (the phrases can appear in a different order in the two sequences).


1



1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 2, 2, 1, 1, 2, 4, 4, 2, 1
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OFFSET

1,8


COMMENTS

The ZivLempel 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.
Equivalent sequences necessarily have the same Hamming weight.
See A106182 for further references and links.


REFERENCES

J. Ziv and A. Lempel, A universal algorithm for sequential data compression. IEEE Trans. Information Theory IT23 (1977), 337343.


LINKS

Table of n, a(n) for n=1..21.


EXAMPLE

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.


CROSSREFS

Row sums give A106182.
Sequence in context: A204260 A122923 A113971 * A291191 A273866 A071202
Adjacent sequences: A109335 A109336 A109337 * A109339 A109340 A109341


KEYWORD

nonn,more,tabl


AUTHOR

N. J. A. Sloane, Aug 24 2005


STATUS

approved



