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A034254
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Triangle read by rows giving T(n,k) = number of inequivalent indecomposable linear [ n,k ] binary codes without 0 columns (n >= 2, 1 <= k <= n).
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33
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1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 3, 5, 3, 1, 1, 4, 10, 10, 4, 1, 1, 5, 18, 28, 18, 5, 1, 1, 7, 31, 71, 71, 31, 7, 1, 1, 8, 51, 165, 250, 165, 51, 8, 1, 1, 10, 79, 361, 809, 809, 361, 79, 10, 1, 1, 12, 121, 754, 2484, 3759, 2484, 754, 121, 12, 1, 1, 14, 177, 1503, 7240, 16749, 16749, 7240, 1503, 177, 14, 1
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OFFSET
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1,8
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COMMENTS
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Fripertinger and Kerber (1995) mention that Slepian (1960) gave a generating function scheme for computing R_{n,k,2} = T(n,k), but it is not always correct. In Theorem 3.1, they give a corrected formula, but it seems too difficult to implement it in Sage. They do provide, however, a SYMMETRICA program for its computation (see the links). - Petros Hadjicostas, Oct 07 2019
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LINKS
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Discrete algorithms at the University of Bayreuth, Symmetrica.
H. Fripertinger and A. Kerber, Isometry classes of indecomposable linear codes. In: G. Cohen, M. Giusti, T. Mora (eds), Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, 11th International Symposium, AAECC 1995, Lect. Notes Comp. Sci. 948 (1995), pp. 194-204. [We have T(n,k) = R_{nk2}; see p. 197.]
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EXAMPLE
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Triangle T(n,k) (with rows n >= 2 and columns k >= 1) begins as follows:
1;
1, 1;
1, 1, 1;
1, 2, 2, 1;
1, 3, 5, 3, 1;
1, 4, 10, 10, 4, 1;
1, 5, 18, 28, 18, 5, 1;
1, 7, 31, 71, 71, 31, 7, 1;
1, 8, 51, 165, 250, 165, 51, 8, 1;
...
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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