a(N,k)  tabf head (staircase) for  A092079  W. Lang, Mar 19, 2004
 
   N   n,m   |k: 1   2   3   4   5   6   7   8   9  10  11  12  13  14  15  16  17  18  19  20  21  22  

   1   1,1   |   1
   
   2   2,1   |   1
   3   2,2   |   1 | 0
   
   4   3,1   |   1
   5   3,2   |   0 | 1
   6   3,3   |   1 | 0 | 0
   
   7   4,1   |   1
   8   4,2   |   1 | 1
   9   4,3   |   0 | 1 | 0
  10   4,4   |   1 | 0   0 | 0 | 0
  
  11   5,1   |   1
  12   5,2   |   0 | 1
  13   5,3   |   0 | 1 | 0
  14   5,4   |   0 | 1   0 | 0 | 0
  15   5,5   |   1 | 0   0 | 0   0 | 0 | 0
  
  16   6,1   |   1
  17   6,2   |   1 | 1
  18   6,3   |   1 | 1 | 1
  19   6,4   |   0 | 1   1 | 0 | 0
  20   6,5   |   0 | 1   0 | 0   0 | 0 | 0
  21   6,6   |   1 | 0   0   0 | 0   0   0 | 0   0 | 0   0
               
  22   7,1   |   1
  23   7,2   |   0 | 1
  24   7,3   |   0 | 1 | 1
  25   7,4   |   0 | 1   0 | 1 | 0
  26   7,5   |   0 | 1   1 | 0   0 | 0 | 0
  27   7,6   |   0 | 1   0   0 | 0   0   0 | 0   0 | 0 | 0
  28   7,7   |   1 | 0   0   0 | 0   0   0   0 | 0   0   0 | 0  0 | 0 | 0

  29   8,1   |   1
  30   8,2   |   1 | 1
  31   8,3   |   0 | 1 | 1
  32   8,4   |   1 | 1   1 | 1 | 0
  33   8,5   |   0 | 1   1 | 1   0 | 0 | 0
  34   8,6   |   0 | 1   1   0 | 0   0   0 | 0   0 | 0 | 0
  35   8,7   |   0 | 1   0   0 | 0   0   0   0 | 0   0   0 | 0   0 | 0 | 0
  36   8,8   |   1 | 0   0   0   0 | 0   0   0   0   0 | 0   0   0   0   0 | 0   0   0 | 0   0 | 0 | 0

  etc.

   N   n,m   |k: 1   2   3   4   5   6   7   8   9  10  11  12  13  14  15  16  17  18  19  20  21  22


  Cf. Abramowitz-Stegun pp. 831-2.

  Example: a(13,2)=1: From the three partitions of 3 only the parts of the second one (in  Abramowitz-Stegun order), i.e. (1,2), 
  are the exponents in partititon of 5 into 3 parts. This is because the two 3-partitions of 5 are [1^2,3^1] and [1^1,2^2].
  There are neither 3-partitions of 5 with exponent 3 nor 1,1,1.

  See A092078 where also the multiplicities are counted.