[seqfan] A005646 triangle (A171872) now linked to A039754

Robert Munafo mrob27 at gmail.com
Sat Jan 2 00:13:16 CET 2010


Andrew Weimholt wrote:

> Robert Munafo wrote:
>
>> In Table 1 on page 3 we find:
>> 1 1 1 1 1
>> 1 1 1 1 1
>> 1 2 3 4 5
>> .. 1 3 6 10
>> .. 1 6 19 47
>> .. .. 3 27 131
>> .. .. 3 50 472
>> .. .. 1 56 1326
>> .. .. 1 74 3779
>> (etc.)
>>
>
> [...]
> This is why the last 2^(k-1) terms agree with the table in the
> block-codes paper.
>
> The table in the can be transposed to generate a triangle and should be
> added
> to the OEIS (when submissions are again allowed).
>


I have created an OEIS entry for three different tables that might be what
you are referring to, and they are available here during the interim:

   www.mrob.com/pub/math/OEIS-extra.txt

The tables are A171876, A171871 and A171872, using A-numbers I reserved with
the dispenser and will submit later. Full text of the first follows; for the
others see the above web page:

%d A171876 20100101.175330
%I A171876
%S A171876
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 A171876
19963,38073,65664,98804,133576,158658,1,1,6,16,103,497,3253,19735,
%U A171876 120843,681474,3561696
%N 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.
%C A171876 This connection was shown by Andrew Weimholt, and can be
described in terms of 2-coloring a J-dimensional hypercube. Dec 30 2009
%C A171876 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 A171876 1
%C A171876 1,1
%C A171876 1,1,3,3
%C A171876 1,1,4,6,19,27,50,56
%C A171876
1,1,5,10,47,131,472,1326,3779,9013,19963,38073,65664,98804,133576,158658
%H A171876 Harald Fripertinger, <a href="
http://www.mathe2.uni-bayreuth.de/frib/html2/construction/blockcodes_2.html">Enumeration
of block codes</a>
%H A171876 R. Munafo, <a
href="http://mrob.com/pub/math/seq-a005646.html">Classifications
of N Elements</a>
%Y A171876 Cf. A039754, A171872, A171871, A005646
%A A171876 Robert Munafo, Jan 01 2010

--
Robert Munafo  --  mrob.com



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