// output of ./demo/comb/composition-nz-left-smooth-demo.cc:
// Description:
//% Left-smooth compositions: compositions of n
//% with maximal up-step <= 1 and first part 1.
//% Lexicographic order.
//% Same as "fountains of coins", see OEIS sequence A005169.

arg 1: 9 == n  [Left-smooth compositions of n]  default=9
arg 2: 0 == aa  [If aa!=0, render as compositions (1) or fountains of coins (2)]  default=0
   1:  [ 1 1 1 1 1 1 1 1 1 ]
   2:  [ 1 1 1 1 1 1 1 2 ]
   3:  [ 1 1 1 1 1 1 2 1 ]
   4:  [ 1 1 1 1 1 2 1 1 ]
   5:  [ 1 1 1 1 1 2 2 ]
   6:  [ 1 1 1 1 2 1 1 1 ]
   7:  [ 1 1 1 1 2 1 2 ]
   8:  [ 1 1 1 1 2 2 1 ]
   9:  [ 1 1 1 1 2 3 ]
  10:  [ 1 1 1 2 1 1 1 1 ]
  11:  [ 1 1 1 2 1 1 2 ]
  12:  [ 1 1 1 2 1 2 1 ]
  13:  [ 1 1 1 2 2 1 1 ]
  14:  [ 1 1 1 2 2 2 ]
  15:  [ 1 1 1 2 3 1 ]
  16:  [ 1 1 2 1 1 1 1 1 ]
  17:  [ 1 1 2 1 1 1 2 ]
  18:  [ 1 1 2 1 1 2 1 ]
  19:  [ 1 1 2 1 2 1 1 ]
  20:  [ 1 1 2 1 2 2 ]
  21:  [ 1 1 2 2 1 1 1 ]
  22:  [ 1 1 2 2 1 2 ]
  23:  [ 1 1 2 2 2 1 ]
  24:  [ 1 1 2 2 3 ]
  25:  [ 1 1 2 3 1 1 ]
  26:  [ 1 1 2 3 2 ]
  27:  [ 1 2 1 1 1 1 1 1 ]
  28:  [ 1 2 1 1 1 1 2 ]
  29:  [ 1 2 1 1 1 2 1 ]
  30:  [ 1 2 1 1 2 1 1 ]
  31:  [ 1 2 1 1 2 2 ]
  32:  [ 1 2 1 2 1 1 1 ]
  33:  [ 1 2 1 2 1 2 ]
  34:  [ 1 2 1 2 2 1 ]
  35:  [ 1 2 1 2 3 ]
  36:  [ 1 2 2 1 1 1 1 ]
  37:  [ 1 2 2 1 1 2 ]
  38:  [ 1 2 2 1 2 1 ]
  39:  [ 1 2 2 2 1 1 ]
  40:  [ 1 2 2 2 2 ]
  41:  [ 1 2 2 3 1 ]
  42:  [ 1 2 3 1 1 1 ]
  43:  [ 1 2 3 1 2 ]
  44:  [ 1 2 3 2 1 ]
  45:  [ 1 2 3 3 ]
 ct=45