// output of ./demo/comb/composition-nz-prefix-cond-demo.cc:
// Description:
//% Compositions of n into positive parts with restricted prefixes.
//% Lexicographic order.

arg 1: 7 == n  [compositions of n (n>=1)]  default=7
arg 2: 5 == c  [Condition function:
      0 ==> all compositions (condition always true),
      1 ==> adjacent digits distinct
      2 ==> up-down
      3 ==> consecutive parts
      4 ==> odd parts
      5 ==> growth condition: a[k] <= 2*a[k-1]
      6 ==> fall condition: 2*a[k] <= a[k-1]
      7 ==> parts are Mersenne numbers
      8 ==> parts are Mersenne numbers, partitions
      9 ==> parts are powers of 2]  default=5
arg 3: 0 == aa  [If aa!=0, render as compositions (1) or fountains of coins (2)]  default=0
 1:  [ 1 1 1 1 1 1 1 ]
 2:  [ 1 1 1 1 1 2 ]
 3:  [ 1 1 1 1 2 1 ]
 4:  [ 1 1 1 2 1 1 ]
 5:  [ 1 1 1 2 2 ]
 6:  [ 1 1 2 1 1 1 ]
 7:  [ 1 1 2 1 2 ]
 8:  [ 1 1 2 2 1 ]
 9:  [ 1 1 2 3 ]
10:  [ 1 2 1 1 1 1 ]
11:  [ 1 2 1 1 2 ]
12:  [ 1 2 1 2 1 ]
13:  [ 1 2 2 1 1 ]
14:  [ 1 2 2 2 ]
15:  [ 1 2 3 1 ]
16:  [ 1 2 4 ]
17:  [ 2 1 1 1 1 1 ]
18:  [ 2 1 1 1 2 ]
19:  [ 2 1 1 2 1 ]
20:  [ 2 1 2 1 1 ]
21:  [ 2 1 2 2 ]
22:  [ 2 2 1 1 1 ]
23:  [ 2 2 1 2 ]
24:  [ 2 2 2 1 ]
25:  [ 2 2 3 ]
26:  [ 2 3 1 1 ]
27:  [ 2 3 2 ]
28:  [ 2 4 1 ]
29:  [ 3 1 1 1 1 ]
30:  [ 3 1 1 2 ]
31:  [ 3 1 2 1 ]
32:  [ 3 2 1 1 ]
33:  [ 3 2 2 ]
34:  [ 3 3 1 ]
35:  [ 3 4 ]
36:  [ 4 1 1 1 ]
37:  [ 4 1 2 ]
38:  [ 4 2 1 ]
39:  [ 4 3 ]
40:  [ 5 1 1 ]
41:  [ 5 2 ]
42:  [ 6 1 ]
43:  [ 7 ]
 ct=43
