// output of ./demo/comb/ascent-rgs-demo.cc: // Description: //% Ascent sequences (restricted growth strings, RGS). //% 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. //% Lexicographic order. //% Cf. OEIS sequence A022493. arg 1: 5 == n [Length of strings] default=5 1: [ . . . . . ] 5 [ . . . . . ] 2: [ . . . . 1 ] 4 [ . . . . 1 ] 3: [ . . . 1 . ] 3 [ . . . 1 1 ] 4: [ . . . 1 1 ] 4 [ . . . 1 1 ] 5: [ . . . 1 2 ] 4 [ . . . 1 2 ] 6: [ . . 1 . . ] 2 [ . . 1 1 1 ] 7: [ . . 1 . 1 ] 4 [ . . 1 1 2 ] 8: [ . . 1 . 2 ] 4 [ . . 1 1 2 ] 9: [ . . 1 1 . ] 3 [ . . 1 1 1 ] 10: [ . . 1 1 1 ] 4 [ . . 1 1 1 ] 11: [ . . 1 1 2 ] 4 [ . . 1 1 2 ] 12: [ . . 1 2 . ] 3 [ . . 1 2 2 ] 13: [ . . 1 2 1 ] 4 [ . . 1 2 2 ] 14: [ . . 1 2 2 ] 4 [ . . 1 2 2 ] 15: [ . . 1 2 3 ] 4 [ . . 1 2 3 ] 16: [ . 1 . . . ] 1 [ . 1 1 1 1 ] 17: [ . 1 . . 1 ] 4 [ . 1 1 1 2 ] 18: [ . 1 . . 2 ] 4 [ . 1 1 1 2 ] 19: [ . 1 . 1 . ] 3 [ . 1 1 2 2 ] 20: [ . 1 . 1 1 ] 4 [ . 1 1 2 2 ] 21: [ . 1 . 1 2 ] 4 [ . 1 1 2 3 ] 22: [ . 1 . 1 3 ] 4 [ . 1 1 2 3 ] 23: [ . 1 . 2 . ] 3 [ . 1 1 2 2 ] 24: [ . 1 . 2 1 ] 4 [ . 1 1 2 2 ] 25: [ . 1 . 2 2 ] 4 [ . 1 1 2 2 ] 26: [ . 1 . 2 3 ] 4 [ . 1 1 2 3 ] 27: [ . 1 1 . . ] 2 [ . 1 1 1 1 ] 28: [ . 1 1 . 1 ] 4 [ . 1 1 1 2 ] 29: [ . 1 1 . 2 ] 4 [ . 1 1 1 2 ] 30: [ . 1 1 1 . ] 3 [ . 1 1 1 1 ] 31: [ . 1 1 1 1 ] 4 [ . 1 1 1 1 ] 32: [ . 1 1 1 2 ] 4 [ . 1 1 1 2 ] 33: [ . 1 1 2 . ] 3 [ . 1 1 2 2 ] 34: [ . 1 1 2 1 ] 4 [ . 1 1 2 2 ] 35: [ . 1 1 2 2 ] 4 [ . 1 1 2 2 ] 36: [ . 1 1 2 3 ] 4 [ . 1 1 2 3 ] 37: [ . 1 2 . . ] 2 [ . 1 2 2 2 ] 38: [ . 1 2 . 1 ] 4 [ . 1 2 2 3 ] 39: [ . 1 2 . 2 ] 4 [ . 1 2 2 3 ] 40: [ . 1 2 . 3 ] 4 [ . 1 2 2 3 ] 41: [ . 1 2 1 . ] 3 [ . 1 2 2 2 ] 42: [ . 1 2 1 1 ] 4 [ . 1 2 2 2 ] 43: [ . 1 2 1 2 ] 4 [ . 1 2 2 3 ] 44: [ . 1 2 1 3 ] 4 [ . 1 2 2 3 ] 45: [ . 1 2 2 . ] 3 [ . 1 2 2 2 ] 46: [ . 1 2 2 1 ] 4 [ . 1 2 2 2 ] 47: [ . 1 2 2 2 ] 4 [ . 1 2 2 2 ] 48: [ . 1 2 2 3 ] 4 [ . 1 2 2 3 ] 49: [ . 1 2 3 . ] 3 [ . 1 2 3 3 ] 50: [ . 1 2 3 1 ] 4 [ . 1 2 3 3 ] 51: [ . 1 2 3 2 ] 4 [ . 1 2 3 3 ] 52: [ . 1 2 3 3 ] 4 [ . 1 2 3 3 ] 53: [ . 1 2 3 4 ] 4 [ . 1 2 3 4 ] ct=53