// output of ./demo/comb/descent-rgs-stats-demo.cc: // Description: //% Statistics for descent sequences. //% A descent sequence is a sequence [d(1), d(2), ..., d(n)] where d(1)=0, //% d(k)>=0, and d(k) <= 1 + desc([d(1), d(2), ..., d(k-1)]) and desc(.) //% counts the number of descents of its argument. //% Cf. the following OEIS sequences: //% A225624: triangle, length-n descent sequences with k-1 descents. arg 1: 5 == n [Length of strings, n>=1] default=5 arg 2: 1 == sq [Select stats: 0 ==> max element 1 ==> number of descents 2 ==> number of ascents 3 ==> number of zeros - 1 4 ==> number of maximal digits - 1 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 10 ==> number of odd values 40 ==> number of flat steps ] default=1 1: [ . . . . . ] 0 2: [ . . . . 1 ] 0 3: [ . . . 1 . ] 1 4: [ . . . 1 1 ] 0 5: [ . . 1 . . ] 1 6: [ . . 1 . 1 ] 1 7: [ . . 1 . 2 ] 1 8: [ . . 1 1 . ] 1 9: [ . . 1 1 1 ] 0 10: [ . 1 . . . ] 1 11: [ . 1 . . 1 ] 1 12: [ . 1 . . 2 ] 1 13: [ . 1 . 1 . ] 2 14: [ . 1 . 1 1 ] 1 15: [ . 1 . 1 2 ] 1 16: [ . 1 . 2 . ] 2 17: [ . 1 . 2 1 ] 2 18: [ . 1 . 2 2 ] 1 19: [ . 1 1 . . ] 1 20: [ . 1 1 . 1 ] 1 21: [ . 1 1 . 2 ] 1 22: [ . 1 1 1 . ] 1 23: [ . 1 1 1 1 ] 0 5, 15, 3, 0, 0, 0, ct=23