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 Ziv-Lempel encodings (the phrases can appear in a different order in the two sequences).

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

Offset

1,8

Comments

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.

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 IT-23 (1977), 337-343.

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