// output of ./demo/comb/composition-nz-subdiagonal-demo.cc:
// Description:
//% Subdiagonal compositions: compositions a[1] + a[2] + ... + a[m] = n
//%   such that a[k] <= k.
//% Lexicographic order.
//% Cf. OEIS sequence A008930.

arg 1: 9 == n  [subdiagonal compositions of n]  default=9
arg 2: 0 == aa  [Whether to render as ASCII art]  default=0
   1:  [ 9]   [ 1 1 1 1 1 1 1 1 1 ]
   2:  [ 8]   [ 1 1 1 1 1 1 1 2 ]
   3:  [ 8]   [ 1 1 1 1 1 1 2 1 ]
   4:  [ 7]   [ 1 1 1 1 1 1 3 ]
   5:  [ 8]   [ 1 1 1 1 1 2 1 1 ]
   6:  [ 7]   [ 1 1 1 1 1 2 2 ]
   7:  [ 7]   [ 1 1 1 1 1 3 1 ]
   8:  [ 6]   [ 1 1 1 1 1 4 ]
   9:  [ 8]   [ 1 1 1 1 2 1 1 1 ]
  10:  [ 7]   [ 1 1 1 1 2 1 2 ]
  11:  [ 7]   [ 1 1 1 1 2 2 1 ]
  12:  [ 6]   [ 1 1 1 1 2 3 ]
  13:  [ 7]   [ 1 1 1 1 3 1 1 ]
  14:  [ 6]   [ 1 1 1 1 3 2 ]
  15:  [ 6]   [ 1 1 1 1 4 1 ]
  16:  [ 5]   [ 1 1 1 1 5 ]
  17:  [ 8]   [ 1 1 1 2 1 1 1 1 ]
  18:  [ 7]   [ 1 1 1 2 1 1 2 ]
  19:  [ 7]   [ 1 1 1 2 1 2 1 ]
  20:  [ 6]   [ 1 1 1 2 1 3 ]
  21:  [ 7]   [ 1 1 1 2 2 1 1 ]
  22:  [ 6]   [ 1 1 1 2 2 2 ]
  23:  [ 6]   [ 1 1 1 2 3 1 ]
  24:  [ 5]   [ 1 1 1 2 4 ]
  25:  [ 7]   [ 1 1 1 3 1 1 1 ]
  26:  [ 6]   [ 1 1 1 3 1 2 ]
  27:  [ 6]   [ 1 1 1 3 2 1 ]
  28:  [ 5]   [ 1 1 1 3 3 ]
  29:  [ 6]   [ 1 1 1 4 1 1 ]
  30:  [ 5]   [ 1 1 1 4 2 ]
  31:  [ 8]   [ 1 1 2 1 1 1 1 1 ]
  32:  [ 7]   [ 1 1 2 1 1 1 2 ]
  33:  [ 7]   [ 1 1 2 1 1 2 1 ]
  34:  [ 6]   [ 1 1 2 1 1 3 ]
  35:  [ 7]   [ 1 1 2 1 2 1 1 ]
  36:  [ 6]   [ 1 1 2 1 2 2 ]
  37:  [ 6]   [ 1 1 2 1 3 1 ]
  38:  [ 5]   [ 1 1 2 1 4 ]
  39:  [ 7]   [ 1 1 2 2 1 1 1 ]
  40:  [ 6]   [ 1 1 2 2 1 2 ]
  41:  [ 6]   [ 1 1 2 2 2 1 ]
  42:  [ 5]   [ 1 1 2 2 3 ]
  43:  [ 6]   [ 1 1 2 3 1 1 ]
  44:  [ 5]   [ 1 1 2 3 2 ]
  45:  [ 5]   [ 1 1 2 4 1 ]
  46:  [ 7]   [ 1 1 3 1 1 1 1 ]
  47:  [ 6]   [ 1 1 3 1 1 2 ]
  48:  [ 6]   [ 1 1 3 1 2 1 ]
  49:  [ 5]   [ 1 1 3 1 3 ]
  50:  [ 6]   [ 1 1 3 2 1 1 ]
  51:  [ 5]   [ 1 1 3 2 2 ]
  52:  [ 5]   [ 1 1 3 3 1 ]
  53:  [ 4]   [ 1 1 3 4 ]
  54:  [ 8]   [ 1 2 1 1 1 1 1 1 ]
  55:  [ 7]   [ 1 2 1 1 1 1 2 ]
  56:  [ 7]   [ 1 2 1 1 1 2 1 ]
  57:  [ 6]   [ 1 2 1 1 1 3 ]
  58:  [ 7]   [ 1 2 1 1 2 1 1 ]
  59:  [ 6]   [ 1 2 1 1 2 2 ]
  60:  [ 6]   [ 1 2 1 1 3 1 ]
  61:  [ 5]   [ 1 2 1 1 4 ]
  62:  [ 7]   [ 1 2 1 2 1 1 1 ]
  63:  [ 6]   [ 1 2 1 2 1 2 ]
  64:  [ 6]   [ 1 2 1 2 2 1 ]
  65:  [ 5]   [ 1 2 1 2 3 ]
  66:  [ 6]   [ 1 2 1 3 1 1 ]
  67:  [ 5]   [ 1 2 1 3 2 ]
  68:  [ 5]   [ 1 2 1 4 1 ]
  69:  [ 7]   [ 1 2 2 1 1 1 1 ]
  70:  [ 6]   [ 1 2 2 1 1 2 ]
  71:  [ 6]   [ 1 2 2 1 2 1 ]
  72:  [ 5]   [ 1 2 2 1 3 ]
  73:  [ 6]   [ 1 2 2 2 1 1 ]
  74:  [ 5]   [ 1 2 2 2 2 ]
  75:  [ 5]   [ 1 2 2 3 1 ]
  76:  [ 4]   [ 1 2 2 4 ]
  77:  [ 6]   [ 1 2 3 1 1 1 ]
  78:  [ 5]   [ 1 2 3 1 2 ]
  79:  [ 5]   [ 1 2 3 2 1 ]
  80:  [ 4]   [ 1 2 3 3 ]
 ct=80