// output of ./demo/comb/ascent-rgs-stats-demo.cc: // Description: //% Statistics for ascent sequences. //% Cf. the following OEIS sequences: //% A218577: //% triangle, length-n ascent sequences with maximal element k-1. //% An ascent sequence is a sequence [d(1), d(2), ..., d(n)] where d(1)=0, d(k)>=0, //% and d(k) <= 1 + asc([d(1), d(2), ..., d(k-1)]) and asc(.) counts the number //% of ascents of its argument. //% A137251: ascent sequences with k ascents. //% A175579: ascent sequences with k zeros. //% A218579: ascent sequences with position of last zero at index k-1. //% A218580: ascent sequences with position of first occurrence of maximal value at index k-1. //% A218581: ascent sequences with position of last occurrence of maximal value at index k-1. arg 1: 5 == n [Length of strings, n>=1] default=5 arg 2: 0 == sq [Select stats: 0 ==> max element 1 ==> number of ascents 2 ==> number of descents 3 ==> number of zeros 4 ==> number of fixed points 5 ==> number of maximal digits 6 ==> position of last occurrence of zero 7 ==> position of first occurrence of the maximal value 8 ==> position of last occurrence of the maximal value 9 ==> number of flat steps 10 ==> number of even values ] default=0 1: [ . . . . . ] 0 2: [ . . . . 1 ] 1 3: [ . . . 1 . ] 1 4: [ . . . 1 1 ] 1 5: [ . . . 1 2 ] 2 6: [ . . 1 . . ] 1 7: [ . . 1 . 1 ] 1 8: [ . . 1 . 2 ] 2 9: [ . . 1 1 . ] 1 10: [ . . 1 1 1 ] 1 11: [ . . 1 1 2 ] 2 12: [ . . 1 2 . ] 2 13: [ . . 1 2 1 ] 2 14: [ . . 1 2 2 ] 2 15: [ . . 1 2 3 ] 3 16: [ . 1 . . . ] 1 17: [ . 1 . . 1 ] 1 18: [ . 1 . . 2 ] 2 19: [ . 1 . 1 . ] 1 20: [ . 1 . 1 1 ] 1 21: [ . 1 . 1 2 ] 2 22: [ . 1 . 1 3 ] 3 23: [ . 1 . 2 . ] 2 24: [ . 1 . 2 1 ] 2 25: [ . 1 . 2 2 ] 2 26: [ . 1 . 2 3 ] 3 27: [ . 1 1 . . ] 1 28: [ . 1 1 . 1 ] 1 29: [ . 1 1 . 2 ] 2 30: [ . 1 1 1 . ] 1 31: [ . 1 1 1 1 ] 1 32: [ . 1 1 1 2 ] 2 33: [ . 1 1 2 . ] 2 34: [ . 1 1 2 1 ] 2 35: [ . 1 1 2 2 ] 2 36: [ . 1 1 2 3 ] 3 37: [ . 1 2 . . ] 2 38: [ . 1 2 . 1 ] 2 39: [ . 1 2 . 2 ] 2 40: [ . 1 2 . 3 ] 3 41: [ . 1 2 1 . ] 2 42: [ . 1 2 1 1 ] 2 43: [ . 1 2 1 2 ] 2 44: [ . 1 2 1 3 ] 3 45: [ . 1 2 2 . ] 2 46: [ . 1 2 2 1 ] 2 47: [ . 1 2 2 2 ] 2 48: [ . 1 2 2 3 ] 3 49: [ . 1 2 3 . ] 3 50: [ . 1 2 3 1 ] 3 51: [ . 1 2 3 2 ] 3 52: [ . 1 2 3 3 ] 3 53: [ . 1 2 3 4 ] 4 1, 15, 25, 11, 1, 0, ct=53