a(n,k)  tabf head (staircase) for  A049085
 
 Maximal part of the partitions of n ordered according to the Abramowitz-Stegun table with increasing number of parts m=1..n 
(ref. given in A049085, p.831-2) 

   n\k   1   2   3   4   5   6   7   8   9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30
 
   1     1   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    

   2     2   1   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

   3     3   2   1   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

   4     4   3   2   2   1   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
 
   5     5   4   3   3   2   2   1   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0

   6     6   5   4   3   4   3   2   3   2   2   1   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0

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

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

   9     9   8   7   6   5   7   6   5   4   5   4   3   6   5   4   4   3   3   5   4   3   3   2   4   3   2   3   2   2   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  23  24  25  26  27  28  29  30


For n=10 the 42 entries are:

[10, 9, 8, 7, 6, 5, 8, 7, 6, 5, 6, 5, 4, 4, 7, 6, 5, 4, 5, 4, 3, 4, 3, 6, 5, 4, 4, 3, 3, 2, 5, 4, 3, 3, 2, 4, 3, 2, 3, 2, 2, 1]

################################################## Abramowitz -Stegun  checks ##################################################


For n=11 the 56 entries are:

[11, 10, 9, 8, 7, 6, 9, 8, 7, 6, 5, 7, 6, 5, 5, 4, 8, 7, 6, 5, 6, 5, 4, 5, 4, 4, 3, 7, 6, 5, 4, 5, 4, 3, 4, 3, 3, 6, 5, 4, 4, 3, 
3, 2, 5, 4, 3, 3, 2, 4, 3, 2, 3, 2, 2, 1]

For n=12 the 77 entries are:

[12, 11, 10, 9, 8, 7, 6, 10, 9, 8, 7, 6, 8, 7, 6, 5, 6, 5, 4, 9, 8, 7, 6, 5, 7, 6, 6, 5, 5, 4, 5, 4, 4, 3, 8, 7, 6, 5, 6, 5, 5, 4,
 4, 4, 4, 3, 3, 7, 6, 5, 4, 5, 4, 3, 4, 3, 3, 2, 6, 5, 4, 4, 3, 3, 2, 5, 4, 3, 3, 2, 4, 3, 2, 3, 2, 2, 1]


For n=13 the 101 entries are:

[13, 12, 11, 10, 9, 8, 7, 11, 10, 9, 8, 7, 6, 9, 8, 7, 6, 7, 6, 5, 5, 10, 9, 8, 7, 6, 8, 7, 7, 6, 5, 6, 5, 4, 6, 5, 5, 4, 4, 9, 8, 
7, 6, 5, 7, 6, 5, 4, 6, 5, 5, 5, 4, 4, 3, 4, 3, 8, 7, 6, 5, 6, 5, 5, 4, 4, 4, 4, 3, 3, 3, 7, 6, 5, 4, 5, 4, 3, 4, 3, 3, 2, 6, 5, 4,
 4, 3, 3, 2, 5, 4, 3, 3, 2, 4, 3, 2, 3, 2, 2, 1]


For n=14 the 135 entries are:

[14, 13, 12, 11, 10, 9, 8, 7, 12, 11, 10, 9, 8, 7, 10, 9, 8, 7, 6, 8, 7, 6, 6, 5, 11, 10, 9, 8, 7, 6, 9, 8, 6, 7, 6, 5, 8, 7, 7, 6,
 5, 6, 5, 5, 4, 5, 4, 10, 9, 8, 7, 6, 8, 7, 5, 6, 5, 4, 7, 6, 6, 6, 5, 5, 5, 4, 4, 4, 4, 3, 9, 8, 7, 6, 5, 7, 6, 4, 6, 5, 5, 5, 3, 5,
 4, 4, 4, 4, 3, 3, 8, 7, 6, 5, 6, 5, 4, 5, 4, 4, 4, 3, 3, 3, 2, 7, 6, 5, 4, 5, 4, 3, 4, 3, 3, 2, 6, 5, 4, 4, 3, 3, 2, 5, 4, 3, 3, 2,
 4, 3, 2, 3, 2, 2, 1]

For n=15 the 176 entries are:

[15, 14, 13, 12, 11, 10, 9, 8, 13, 12, 11, 10, 9, 8, 7, 11, 10, 9, 8, 7, 9, 8, 7, 6, 7, 6, 5, 12, 11, 10, 9, 8, 7, 10, 9, 9, 8, 7,
 6, 8, 7, 6, 6, 5, 8, 7, 6, 7, 6, 5, 6, 5, 5, 4, 11, 10, 9, 8, 7, 6, 9, 8, 5, 5, 8, 7, 6, 7, 6, 7, 7, 6, 5, 6, 6, 5, 5, 4, 5, 4, 5,
 4, 4, 3, 10, 9, 8, 7, 6, 8, 7, 5, 4, 7, 6, 6, 6, 6, 5, 5, 5, 4, 5, 5, 4, 4, 4, 4, 3, 3, 9, 8, 7, 6, 5, 7, 6, 5, 4, 6, 5, 5, 3, 5, 4,
 4, 4, 4, 3, 3, 3, 8, 7, 6, 5, 6, 5, 4, 5, 4, 4, 4, 3, 3, 3, 2, 7, 6, 5, 4, 5, 4, 3, 4, 3, 3, 2, 6, 5, 4, 4, 3, 3, 2, 5, 4, 3, 3, 2,
 4, 3, 2, 3, 2, 2, 1]

...


#################################################################################################################################