// output of ./demo/comb/descent-rgs-demo.cc: // Description: //% Descent sequences (restricted growth strings, RGS). //% 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. //% Lexicographic order. //% See OEIS sequence A225588. arg 1: 6 == n [Length of strings] default=6 1: [ . . . . . . ] [ . . . . . . ] 0 2: [ . . . . . 1 ] [ . . . . . . ] 5 3: [ . . . . 1 . ] [ . . . . . 1 ] 4 4: [ . . . . 1 1 ] [ . . . . . . ] 5 5: [ . . . 1 . . ] [ . . . . 1 1 ] 3 6: [ . . . 1 . 1 ] [ . . . . 1 1 ] 5 7: [ . . . 1 . 2 ] [ . . . . 1 1 ] 5 8: [ . . . 1 1 . ] [ . . . . . 1 ] 4 9: [ . . . 1 1 1 ] [ . . . . . . ] 5 10: [ . . 1 . . . ] [ . . . 1 1 1 ] 2 11: [ . . 1 . . 1 ] [ . . . 1 1 1 ] 5 12: [ . . 1 . . 2 ] [ . . . 1 1 1 ] 5 13: [ . . 1 . 1 . ] [ . . . 1 1 2 ] 4 14: [ . . 1 . 1 1 ] [ . . . 1 1 1 ] 5 15: [ . . 1 . 1 2 ] [ . . . 1 1 1 ] 5 16: [ . . 1 . 2 . ] [ . . . 1 1 2 ] 4 17: [ . . 1 . 2 1 ] [ . . . 1 1 2 ] 5 18: [ . . 1 . 2 2 ] [ . . . 1 1 1 ] 5 19: [ . . 1 1 . . ] [ . . . . 1 1 ] 3 20: [ . . 1 1 . 1 ] [ . . . . 1 1 ] 5 21: [ . . 1 1 . 2 ] [ . . . . 1 1 ] 5 22: [ . . 1 1 1 . ] [ . . . . . 1 ] 4 23: [ . . 1 1 1 1 ] [ . . . . . . ] 5 24: [ . 1 . . . . ] [ . . 1 1 1 1 ] 1 25: [ . 1 . . . 1 ] [ . . 1 1 1 1 ] 5 26: [ . 1 . . . 2 ] [ . . 1 1 1 1 ] 5 27: [ . 1 . . 1 . ] [ . . 1 1 1 2 ] 4 28: [ . 1 . . 1 1 ] [ . . 1 1 1 1 ] 5 29: [ . 1 . . 1 2 ] [ . . 1 1 1 1 ] 5 30: [ . 1 . . 2 . ] [ . . 1 1 1 2 ] 4 31: [ . 1 . . 2 1 ] [ . . 1 1 1 2 ] 5 32: [ . 1 . . 2 2 ] [ . . 1 1 1 1 ] 5 33: [ . 1 . 1 . . ] [ . . 1 1 2 2 ] 3 34: [ . 1 . 1 . 1 ] [ . . 1 1 2 2 ] 5 35: [ . 1 . 1 . 2 ] [ . . 1 1 2 2 ] 5 36: [ . 1 . 1 . 3 ] [ . . 1 1 2 2 ] 5 37: [ . 1 . 1 1 . ] [ . . 1 1 1 2 ] 4 38: [ . 1 . 1 1 1 ] [ . . 1 1 1 1 ] 5 39: [ . 1 . 1 1 2 ] [ . . 1 1 1 1 ] 5 40: [ . 1 . 1 2 . ] [ . . 1 1 1 2 ] 4 41: [ . 1 . 1 2 1 ] [ . . 1 1 1 2 ] 5 42: [ . 1 . 1 2 2 ] [ . . 1 1 1 1 ] 5 43: [ . 1 . 2 . . ] [ . . 1 1 2 2 ] 3 44: [ . 1 . 2 . 1 ] [ . . 1 1 2 2 ] 5 45: [ . 1 . 2 . 2 ] [ . . 1 1 2 2 ] 5 46: [ . 1 . 2 . 3 ] [ . . 1 1 2 2 ] 5 47: [ . 1 . 2 1 . ] [ . . 1 1 2 3 ] 4 48: [ . 1 . 2 1 1 ] [ . . 1 1 2 2 ] 5 49: [ . 1 . 2 1 2 ] [ . . 1 1 2 2 ] 5 50: [ . 1 . 2 1 3 ] [ . . 1 1 2 2 ] 5 51: [ . 1 . 2 2 . ] [ . . 1 1 1 2 ] 4 52: [ . 1 . 2 2 1 ] [ . . 1 1 1 2 ] 5 53: [ . 1 . 2 2 2 ] [ . . 1 1 1 1 ] 5 54: [ . 1 1 . . . ] [ . . . 1 1 1 ] 2 55: [ . 1 1 . . 1 ] [ . . . 1 1 1 ] 5 56: [ . 1 1 . . 2 ] [ . . . 1 1 1 ] 5 57: [ . 1 1 . 1 . ] [ . . . 1 1 2 ] 4 58: [ . 1 1 . 1 1 ] [ . . . 1 1 1 ] 5 59: [ . 1 1 . 1 2 ] [ . . . 1 1 1 ] 5 60: [ . 1 1 . 2 . ] [ . . . 1 1 2 ] 4 61: [ . 1 1 . 2 1 ] [ . . . 1 1 2 ] 5 62: [ . 1 1 . 2 2 ] [ . . . 1 1 1 ] 5 63: [ . 1 1 1 . . ] [ . . . . 1 1 ] 3 64: [ . 1 1 1 . 1 ] [ . . . . 1 1 ] 5 65: [ . 1 1 1 . 2 ] [ . . . . 1 1 ] 5 66: [ . 1 1 1 1 . ] [ . . . . . 1 ] 4 67: [ . 1 1 1 1 1 ] [ . . . . . . ] 5 ct=67