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.

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, 19963, 38073, 65664, 98804, 133576, 158658, 1, 1, 6, 16, 103, 497, 3253, 19735, 120843, 681474, 3561696

Offset: 0

Author

Robert Munafo, Jan 21 2010

Keywords

• nonn

Comments

This connection was conjectured by Robert Munafo, then proved by Andrew Weimholt.

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

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

1

1,1

1,1,3,3

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

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

Links

• Harald Fripertinger, Enumeration of block codes
• R. Munafo, Classifications of N Elements

Crossrefs

Cf. A039754, A171872, A171871, A005646.