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A171876 Mutual solutions to two classification counting problems: binary block codes of wordlength J with N used words; and classifications of N elements by J partitions. 3

%I

%S 1,1,1,1,1,3,3,1,1,4,6,19,27,50,56,1,1,5,10,47,131,472,1326,3779,9013,

%T 19963,38073,65664,98804,133576,158658,1,1,6,16,103,497,3253,19735,

%U 120843,681474,3561696

%N Mutual solutions to two classification counting problems: binary block codes of wordlength J with N used words; and classifications of N elements by J partitions.

%C This connection was conjectured by _Robert Munafo_, then proved by _Andrew Weimholt_.

%C A(n) counts 2-colorings of a J-dimensional hypercube with N red vertices and 2^J-N black, each edge has at most one red vertex. - _Andrew Weimholt_, Dec 30 2009

%C This sequence contains terms of A039754 that are found in A171871/A171872. They occur in blocks of length 2^(J-1) as shown here:

%C 1

%C 1,1

%C 1,1,3,3

%C 1,1,4,6,19,27,50,56

%C 1,1,5,10,47,131,472,1326,3779,9013,19963,38073,65664,98804,133576,158658

%H Harald Fripertinger, <a href="http://www.mathe2.uni-bayreuth.de/frib/html2/construction/blockcodes_2.html">Enumeration of block codes</a>

%H R. Munafo, <a href="http://mrob.com/pub/math/seq-a005646.html">Classifications of N Elements</a>

%Y Cf. A039754, A171872, A171871, A005646.

%K nonn

%O 0,6

%A _Robert Munafo_, Jan 21 2010

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Last modified April 21 04:42 EDT 2021. Contains 343146 sequences. (Running on oeis4.)