// output of ./demo/comb/balanced-ordered-tree-lev-seq-stats-demo.cc:
// Description:
//% Statistics for (level sequences of) ordered balanced rooted trees.
//% Cf. the following OEIS sequences:
//% A079500 and A007059: all trees.
//% A048887: trees by height.

arg 1: 8 == n  [Number of non-root nodes]  default=8
arg 2: 0 == sq  [Select stats:
    0 ==> by height
    1 ==> number of ascents
    2 ==> number of descents
    3 ==> number of ones
    4 ==> number of fixed points
    5 ==> number of maximal levels
    6 ==> position of last occurrence of one
    7 ==> position of first occurrence of the maximal value
    9 ==> number of flat steps
   10 ==> number of even values
   11 ==> number of odd values
   20 ==> number of flat steps
   21 ==> number of non-flat steps
   25 ==> number of peaks
]  default=0
arg 3: 0 == aa  [Whether to render trees as ASCII art]  default=0
   1:  [ 0 1 1 1 1 1 1 1 1 ]   1
   2:  [ 0 1 2 1 2 1 2 1 2 ]   2
   3:  [ 0 1 2 1 2 1 2 2 2 ]   2
   4:  [ 0 1 2 1 2 2 1 2 2 ]   2
   5:  [ 0 1 2 1 2 2 2 1 2 ]   2
   6:  [ 0 1 2 1 2 2 2 2 2 ]   2
   7:  [ 0 1 2 2 1 2 1 2 2 ]   2
   8:  [ 0 1 2 2 1 2 2 1 2 ]   2
   9:  [ 0 1 2 2 1 2 2 2 2 ]   2
  10:  [ 0 1 2 2 2 1 2 1 2 ]   2
  11:  [ 0 1 2 2 2 1 2 2 2 ]   2
  12:  [ 0 1 2 2 2 2 1 2 2 ]   2
  13:  [ 0 1 2 2 2 2 2 1 2 ]   2
  14:  [ 0 1 2 2 2 2 2 2 2 ]   2
  15:  [ 0 1 2 3 1 2 3 2 3 ]   3
  16:  [ 0 1 2 3 1 2 3 3 3 ]   3
  17:  [ 0 1 2 3 2 3 1 2 3 ]   3
  18:  [ 0 1 2 3 2 3 2 3 3 ]   3
  19:  [ 0 1 2 3 2 3 3 2 3 ]   3
  20:  [ 0 1 2 3 2 3 3 3 3 ]   3
  21:  [ 0 1 2 3 3 1 2 3 3 ]   3
  22:  [ 0 1 2 3 3 2 3 2 3 ]   3
  23:  [ 0 1 2 3 3 2 3 3 3 ]   3
  24:  [ 0 1 2 3 3 3 1 2 3 ]   3
  25:  [ 0 1 2 3 3 3 2 3 3 ]   3
  26:  [ 0 1 2 3 3 3 3 2 3 ]   3
  27:  [ 0 1 2 3 3 3 3 3 3 ]   3
  28:  [ 0 1 2 3 4 1 2 3 4 ]   4
  29:  [ 0 1 2 3 4 2 3 4 4 ]   4
  30:  [ 0 1 2 3 4 3 4 3 4 ]   4
  31:  [ 0 1 2 3 4 3 4 4 4 ]   4
  32:  [ 0 1 2 3 4 4 2 3 4 ]   4
  33:  [ 0 1 2 3 4 4 3 4 4 ]   4
  34:  [ 0 1 2 3 4 4 4 3 4 ]   4
  35:  [ 0 1 2 3 4 4 4 4 4 ]   4
  36:  [ 0 1 2 3 4 5 3 4 5 ]   5
  37:  [ 0 1 2 3 4 5 4 5 5 ]   5
  38:  [ 0 1 2 3 4 5 5 4 5 ]   5
  39:  [ 0 1 2 3 4 5 5 5 5 ]   5
  40:  [ 0 1 2 3 4 5 6 5 6 ]   6
  41:  [ 0 1 2 3 4 5 6 6 6 ]   6
  42:  [ 0 1 2 3 4 5 6 7 7 ]   7
  43:  [ 0 1 2 3 4 5 6 7 8 ]   8
0, 1, 13, 13, 8, 4, 2, 1, 1, 0, 
 ct=43