W. Lang Oct 09 2008

A145361 tabf array: partition numbers  M31hat(-1).

Partitions of n listed in Abramowitz-Stegun order p. 831-2 (see the main page for an A-number with the reference).
 

   n\k     1       2      3      4       5      6       7       8       9      10     11     12     13     14    15    16    17    18   19   20   21  22 ...  

    
   1       1       0      0      0       0      0       0       0       0       0      0      0      0      0     0     0     0     0    0    0    0   0 
     
   2       1       1      0      0       0      0       0       0       0       0      0      0      0      0     0     0     0     0    0    0    0   0 
  
   3       0       1      1      0       0      0       0       0       0       0      0      0      0      0     0     0     0     0    0    0    0   0
    
   4       0       0      1      1       1      0       0       0       0       0      0      0      0      0     0     0     0     0    0    0    0   0  
 
   5       0       0      0      0       1      1       1       0       0       0      0      0      0      0     0     0     0     0    0    0    0   0 
        
   6       0       0      0      0       0      0       1       0       1       1      1      0      0      0     0     0     0     0    0    0    0   0  
 
   7       0       0      0      0       0      0       0       0       0       0      1      0      1      1     1     0     0     0    0    0    0   0  
  
   8       0       0      0      0       0      0       0       0       0       0      0      0      0      0     1     0     0     1    0    1    1   1    
   .                                                                                                                       .
   .
   .

   n\k     1       2      3      4       5      6       7       8       9      10     11     12     13     14    15    16    17    18   19   20   21  22 ...     
    


The next two rows, for n=9 and n=10, are:

n=9: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1],

n=10: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1].



The row sums give, for n>=1, A004526(n+2): [1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6,...].
They coincide with the row sums of triangle A145362 = S1hat(-1).


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