// output of ./demo/comb/rgs-fincr-demo.cc:
// Description:
//% All restricted growth strings (RGS) s[0,...,n-1]
//%   so that  s[k] <= F[j]+i  where
//%  F[0]=i, F[j+1]=( a[j+1]-a[j]==i ?  F[j]+i : F[j] )
//% Lexicographic order

arg 1: 4 == n  [Length of restricted growth strings]  default=4
arg 2: 2 == i  [Increment allowed (1==> set partitions)]  default=2
  1:  [ 0 0 0 0 ]    [ 0 0 0 0 ]
  2:  [ 0 0 0 1 ]    [ 0 0 0 0 ]
  3:  [ 0 0 0 2 ]    [ 0 0 0 2 ]
  4:  [ 0 0 1 0 ]    [ 0 0 0 0 ]
  5:  [ 0 0 1 1 ]    [ 0 0 0 0 ]
  6:  [ 0 0 1 2 ]    [ 0 0 0 2 ]
  7:  [ 0 0 2 0 ]    [ 0 0 2 2 ]
  8:  [ 0 0 2 1 ]    [ 0 0 2 2 ]
  9:  [ 0 0 2 2 ]    [ 0 0 2 2 ]
 10:  [ 0 0 2 3 ]    [ 0 0 2 2 ]
 11:  [ 0 0 2 4 ]    [ 0 0 2 4 ]
 12:  [ 0 1 0 0 ]    [ 0 0 0 0 ]
 13:  [ 0 1 0 1 ]    [ 0 0 0 0 ]
 14:  [ 0 1 0 2 ]    [ 0 0 0 2 ]
 15:  [ 0 1 1 0 ]    [ 0 0 0 0 ]
 16:  [ 0 1 1 1 ]    [ 0 0 0 0 ]
 17:  [ 0 1 1 2 ]    [ 0 0 0 2 ]
 18:  [ 0 1 2 0 ]    [ 0 0 2 2 ]
 19:  [ 0 1 2 1 ]    [ 0 0 2 2 ]
 20:  [ 0 1 2 2 ]    [ 0 0 2 2 ]
 21:  [ 0 1 2 3 ]    [ 0 0 2 2 ]
 22:  [ 0 1 2 4 ]    [ 0 0 2 4 ]
 23:  [ 0 2 0 0 ]    [ 0 2 2 2 ]
 24:  [ 0 2 0 1 ]    [ 0 2 2 2 ]
 25:  [ 0 2 0 2 ]    [ 0 2 2 2 ]
 26:  [ 0 2 0 3 ]    [ 0 2 2 2 ]
 27:  [ 0 2 0 4 ]    [ 0 2 2 4 ]
 28:  [ 0 2 1 0 ]    [ 0 2 2 2 ]
 29:  [ 0 2 1 1 ]    [ 0 2 2 2 ]
 30:  [ 0 2 1 2 ]    [ 0 2 2 2 ]
 31:  [ 0 2 1 3 ]    [ 0 2 2 2 ]
 32:  [ 0 2 1 4 ]    [ 0 2 2 4 ]
 33:  [ 0 2 2 0 ]    [ 0 2 2 2 ]
 34:  [ 0 2 2 1 ]    [ 0 2 2 2 ]
 35:  [ 0 2 2 2 ]    [ 0 2 2 2 ]
 36:  [ 0 2 2 3 ]    [ 0 2 2 2 ]
 37:  [ 0 2 2 4 ]    [ 0 2 2 4 ]
 38:  [ 0 2 3 0 ]    [ 0 2 2 2 ]
 39:  [ 0 2 3 1 ]    [ 0 2 2 2 ]
 40:  [ 0 2 3 2 ]    [ 0 2 2 2 ]
 41:  [ 0 2 3 3 ]    [ 0 2 2 2 ]
 42:  [ 0 2 3 4 ]    [ 0 2 2 4 ]
 43:  [ 0 2 4 0 ]    [ 0 2 4 4 ]
 44:  [ 0 2 4 1 ]    [ 0 2 4 4 ]
 45:  [ 0 2 4 2 ]    [ 0 2 4 4 ]
 46:  [ 0 2 4 3 ]    [ 0 2 4 4 ]
 47:  [ 0 2 4 4 ]    [ 0 2 4 4 ]
 48:  [ 0 2 4 5 ]    [ 0 2 4 4 ]
 49:  [ 0 2 4 6 ]    [ 0 2 4 6 ]
 ct = 49