// output of ./demo/comb/id-tree-lev-seq-stats-demo.cc:
// Description:
//% Statistics for (level sequences of) unordered rooted identity trees.
//% Cf. the following OEIS sequences:
//% A004111: all identity trees.
//% A227819: identity trees by height.
//% A055327: identity trees by number of descents.
//% A227774: identity trees by number of ones.
//% A244523: identity trees by maximal branching number (out-degree).

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
    5 ==> number of maximal levels
    6 ==> position of last occurrence of one
    8 ==> position of last occurrence of the maximal value
   10 ==> number of even values
   11 ==> number of odd values
   25 ==> number of peaks
]  default=0
arg 3: 0 == aa  [Whether to render trees as ASCII art]  default=0
   1:  [ 0 1 2 3 4 5 6 7 8 ]   8
   2:  [ 0 1 2 3 4 5 6 7 6 ]   7
   3:  [ 0 1 2 3 4 5 6 7 5 ]   7
   4:  [ 0 1 2 3 4 5 6 7 4 ]   7
   5:  [ 0 1 2 3 4 5 6 7 3 ]   7
   6:  [ 0 1 2 3 4 5 6 7 2 ]   7
   7:  [ 0 1 2 3 4 5 6 7 1 ]   7
   8:  [ 0 1 2 3 4 5 6 5 4 ]   6
   9:  [ 0 1 2 3 4 5 6 5 3 ]   6
  10:  [ 0 1 2 3 4 5 6 5 2 ]   6
  11:  [ 0 1 2 3 4 5 6 5 1 ]   6
  12:  [ 0 1 2 3 4 5 6 4 5 ]   6
  13:  [ 0 1 2 3 4 5 6 4 3 ]   6
  14:  [ 0 1 2 3 4 5 6 4 2 ]   6
  15:  [ 0 1 2 3 4 5 6 4 1 ]   6
  16:  [ 0 1 2 3 4 5 6 3 4 ]   6
  17:  [ 0 1 2 3 4 5 6 3 2 ]   6
  18:  [ 0 1 2 3 4 5 6 3 1 ]   6
  19:  [ 0 1 2 3 4 5 6 2 3 ]   6
  20:  [ 0 1 2 3 4 5 6 2 1 ]   6
  21:  [ 0 1 2 3 4 5 6 1 2 ]   6
  22:  [ 0 1 2 3 4 5 4 3 4 ]   5
  23:  [ 0 1 2 3 4 5 4 3 2 ]   5
  24:  [ 0 1 2 3 4 5 4 3 1 ]   5
  25:  [ 0 1 2 3 4 5 4 2 3 ]   5
  26:  [ 0 1 2 3 4 5 4 2 1 ]   5
  27:  [ 0 1 2 3 4 5 4 1 2 ]   5
  28:  [ 0 1 2 3 4 5 3 4 3 ]   5
  29:  [ 0 1 2 3 4 5 3 4 2 ]   5
  30:  [ 0 1 2 3 4 5 3 4 1 ]   5
  31:  [ 0 1 2 3 4 5 3 2 3 ]   5
  32:  [ 0 1 2 3 4 5 3 2 1 ]   5
  33:  [ 0 1 2 3 4 5 3 1 2 ]   5
  34:  [ 0 1 2 3 4 5 2 3 4 ]   5
  35:  [ 0 1 2 3 4 5 2 3 2 ]   5
  36:  [ 0 1 2 3 4 5 2 3 1 ]   5
  37:  [ 0 1 2 3 4 5 2 1 2 ]   5
  38:  [ 0 1 2 3 4 5 1 2 3 ]   5
  39:  [ 0 1 2 3 4 5 1 2 1 ]   5
  40:  [ 0 1 2 3 4 3 2 3 4 ]   4
  41:  [ 0 1 2 3 4 3 2 3 2 ]   4
  42:  [ 0 1 2 3 4 3 2 3 1 ]   4
  43:  [ 0 1 2 3 4 3 2 1 2 ]   4
  44:  [ 0 1 2 3 4 3 1 2 3 ]   4
  45:  [ 0 1 2 3 4 3 1 2 1 ]   4
  46:  [ 0 1 2 3 4 2 3 2 1 ]   4
  47:  [ 0 1 2 3 4 2 3 1 2 ]   4
  48:  [ 0 1 2 3 4 2 1 2 3 ]   4
  49:  [ 0 1 2 3 4 2 1 2 1 ]   4
  50:  [ 0 1 2 3 4 1 2 3 2 ]   4
  51:  [ 0 1 2 3 4 1 2 3 1 ]   4
  52:  [ 0 1 2 3 2 1 2 3 1 ]   3
0, 0, 0, 1, 12, 18, 14, 6, 1, 
 ct=52
