%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 2colorings of a Jdimensional hypercube with N red vertices and 2^JN 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^(J1) 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.unibayreuth.de/frib/html2/construction/blockcodes_2.html">Enumeration of block codes</a>
%H R. Munafo, <a href="http://mrob.com/pub/math/seqa005646.html">Classifications of N Elements</a>
%Y Cf. A039754, A171872, A171871, A005646.
%K nonn
%O 0,6
%A _Robert Munafo_, Jan 21 2010
