// output of ./demo/comb/motzkin-step-rgs-lex-demo.cc: // Description: //% Motzkin step RGS (restricted growth strings), lexicographic order. //% RGS are a[] such that a[k] >= a[k-1] (weakly ascending), a[k]<=k, and //% a[k] - a[k-1] != 1 (no increments by 1). //% Same as: rising factorial numbers where the digits are sorted //% where increments by 1 are disallowed. //% Cf. OEIS sequence A001006. arg 1: 6 == n [Motzkin (step-)RGS for paths from (0,0) to (n,n)] default=6 arg 2: 0 == pq [Whether do draw path (as ASCII art)] default=0 1: [ . . . . . . ] 0 2: [ . . . . . 2 ] 6 3: [ . . . . . 3 ] 6 4: [ . . . . . 4 ] 6 5: [ . . . . . 5 ] 6 6: [ . . . . . 6 ] 6 7: [ . . . . 2 2 ] 5 8: [ . . . . 2 4 ] 6 9: [ . . . . 2 5 ] 6 10: [ . . . . 2 6 ] 6 11: [ . . . . 3 3 ] 5 12: [ . . . . 3 5 ] 6 13: [ . . . . 3 6 ] 6 14: [ . . . . 4 4 ] 5 15: [ . . . . 4 6 ] 6 16: [ . . . . 5 5 ] 5 17: [ . . . 2 2 2 ] 4 18: [ . . . 2 2 4 ] 6 19: [ . . . 2 2 5 ] 6 20: [ . . . 2 2 6 ] 6 21: [ . . . 2 4 4 ] 5 22: [ . . . 2 4 6 ] 6 23: [ . . . 2 5 5 ] 5 24: [ . . . 3 3 3 ] 4 25: [ . . . 3 3 5 ] 6 26: [ . . . 3 3 6 ] 6 27: [ . . . 3 5 5 ] 5 28: [ . . . 4 4 4 ] 4 29: [ . . . 4 4 6 ] 6 30: [ . . 2 2 2 2 ] 3 31: [ . . 2 2 2 4 ] 6 32: [ . . 2 2 2 5 ] 6 33: [ . . 2 2 2 6 ] 6 34: [ . . 2 2 4 4 ] 5 35: [ . . 2 2 4 6 ] 6 36: [ . . 2 2 5 5 ] 5 37: [ . . 2 4 4 4 ] 4 38: [ . . 2 4 4 6 ] 6 39: [ . . 3 3 3 3 ] 3 40: [ . . 3 3 3 5 ] 6 41: [ . . 3 3 3 6 ] 6 42: [ . . 3 3 5 5 ] 5 43: [ . 2 2 2 2 2 ] 2 44: [ . 2 2 2 2 4 ] 6 45: [ . 2 2 2 2 5 ] 6 46: [ . 2 2 2 2 6 ] 6 47: [ . 2 2 2 4 4 ] 5 48: [ . 2 2 2 4 6 ] 6 49: [ . 2 2 2 5 5 ] 5 50: [ . 2 2 4 4 4 ] 4 51: [ . 2 2 4 4 6 ] 6 ct=51