T(n,m)  tabf head (staircase) for  A097305

  Number of partitions of n into odd parts not exceeding  2*m-1 for m=1,2,...,ceiling(n/2) 
    
     \k
  
    n\m         1         2         3         4         5         6         7         8         9
 
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    1         1         0         0         0         0         0         0         0         0
    
    2         1         0         0         0         0         0         0         0         0

    3         1         2         0         0         0         0         0         0         0

    4         1         2         0         0         0         0         0         0         0

    5         1         2         3         0         0         0         0         0         0

    6         1         3         4         0         0         0         0         0         0

    7         1         3         4         5         0         0         0         0         0

    8         1         3         5         6         0         0         0         0         0

    9         1         4         6         7         8         0         0         0         0

   10         1         4         7         9        10         0         0         0         0

   11         1         4         8        10        11        12         0         0         0

   12         1         5         9        12        14        15         0         0         0

   13         1         5        10        14        16        17        18         0         0

   14         1         5        11        16        19        21        22         0         0

   15         1         6        13        19        23        25        26        27         0

   16         1         6        14        21        26        29        31        32         0

   17         1         6        15        24        30        34        36        37        38

   18         1         7        17        27        35        40        43        45        46

   etc.


   E.g.: T(8,3) = 5: there are five partitions of 8 with parts from {1,3,5},
   
   namely (1^8), (1^5,3), (1^2,3^2), (1^3,5) and (3,5).