A057580 and A105633 - Same?

[Paul D. Hanna]

Dear Seqfans,
     Are sequences A057580 and A105633 the same? 
Can anyone determine the answer to this question?
 
Below I describe the sequences more fully.
Thanks for any clues, 
    Paul
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    Consider the maximal and minimal "numbers of codewords 
in mixed code with 2 binary coordinates and n ternary 
coordinates with Hamming distance 3", given at:
 
http://www.tcs.hut.fi/~pat/23.html
 
Among the codes listed there, we are interested in 
the minimal and maximal of the numbers preceeding the ':'
in the following subset (see link for explanation): 
(2,1,3)1: 1 code 
(2,1,3)2: 1 code 
 
(2,2,3)3: 2 codes 
(2,2,3)4: 1 code 
 
(2,3,3)7: 66 codes 
(2,3,3)8: 14 codes 
(2,3,3)9: 3 codes 
 
(2,4,3)19: 25703 codes 
(2,4,3)20: 668 codes 
(2,4,3)21: 23 codes 
(2,4,3)22: 2 codes 
  
The minimal numbers are: 1,3,7,19, ? 
 
and the maximal numbers are: 1,2,4,9,22, ? 
 
The maximal numbers are given by: A057580
http://www.research.att.com/projects/OEIS?Anum=A057580
 
and I guess that the minimal numbers form A002426 
(Central trinomial coefficients) offset 1.
 
Based on this guess, I wonder if the maximal numbers (A057580)
are also equal to A105633:
http://www.research.att.com/projects/OEIS?Anum=A105633
Sequence:  
1,2,4,9,22,57,154,429,1223,3550,10455,31160,93802,284789,..
       
A105633 equals the row sums of triangle A105632, 
where triangle A105632 is defined by:
http://www.research.att.com/projects/OEIS?Anum=A105632
1;
1,1;
2,1,1;
4,3,1,1;
9,7,4,1,1;
21,19,10,5,1,1;
51,51,31,13,6,1,1;
127,141,91,45,16,7,1,1;
323,393,276,141,61,19,8,1,1;
835,1107,834,461,201,79,22,9,1,1; ...

where:
column 0 is A001006 (Motzkin numbers)
column 1 is A002426 (Central trinomial coefficients).

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END