// 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