Search: id:A076831
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%I A076831
%S A076831 1,1,1,1,2,1,1,3,3,1,1,4,6,4,1,1,5,10,10,5,1,1,6,16,22,16,6,1,1,7,
%T A076831 23,43,43,23,7,1,1,8,32,77,106,77,32,8,1,1,9,43,131,240,240,131,43,
%U A076831 9,1,1,10,56,213,516,705,516,213,56,10,1,1,11,71,333,1060,1988,1988
%N A076831 Triangle T(n,k) read by rows giving number of inequivalent binary linear 
               [n,k] codes (n >= 0, 0 <= k <= n).
%C A076831 "The familiar appearance of the first few rows [...] provides a good 
               example of the perils of too hasty extrapolation in mathematics." 
               - Slepian.
%D A076831 H. Fripertinger and A. Kerber, in AAECC-11, Lect. Notes Comp. Sci. 948 
               (1995), 194-204.
%D A076831 Kent E. Morrison, Integer Sequences and Matrices Over Finite Fields, 
               Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.1.
%D A076831 D. Slepian, Some further theory of group codes. Bell System Tech. J. 
               39 1960 1219-1252.
%D A076831 M. Wild, Enumeration of binary and ternary matroids and other applications 
               of the Brylawski-Lucas Theorem, Preprint Nr. 1693, Tech. Hochschule 
               Darmstadt, 1994
%D A076831 M. Wild, Consequences of the Brylawski-Lucas Theorem for binary matroids, 
               European Journal of Combinatorics 17 (1996) 309-316.
%D A076831 M. Wild, The asymptotic number of inequivalent binary codes and nonisomorphic 
               binary matroids, Finite Fields and their Applications 6 (2000) 192-202.
%H A076831 H. Fripertinger, <a href="http://www.mathe2.uni-bayreuth.de/frib/codes/
               tables.html">Isometry Classes of Codes</a>
%H A076831 <a href="Sindx_Coa.html#codes_binary_linear">Index entries for sequences 
               related to binary linear codes</a>
%e A076831 1; 1,1; 1,2,1; 1,3,3,1; 1,4,6,4,1; 1,5,10,10,5; 1,1,6,16,22,16,6,1; ...
%Y A076831 Cf. A022166, A006116, A076766 (row sums). A034356 gives same table but 
               with k=0 column omitted.
%Y A076831 Sequence in context: A108086 A130595 A108363 this_sequence A119724 A162424 
               A008571
%Y A076831 Adjacent sequences: A076828 A076829 A076830 this_sequence A076832 A076833 
               A076834
%K A076831 nonn,tabl,nice
%O A076831 0,5
%A A076831 N. J. A. Sloane (njas(AT)research.att.com), Nov 21 2002

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