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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
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

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

Table of n, a(n) for n=0..41.

Harald Fripertinger, Enumeration of block codes

R. Munafo, Classifications of N Elements

CROSSREFS

Cf. A039754, A171872, A171871, A005646

Sequence in context: A109439 A247646 A133333 * A133332 A179680 A123562

Adjacent sequences:  A171873 A171874 A171875 * A171877 A171878 A171879

KEYWORD

nonn

AUTHOR

Robert Munafo, Jan 21 2010

STATUS

approved

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Last modified May 27 11:14 EDT 2017. Contains 287204 sequences.