// output of ./demo/comb/catalan-step-rgs-lex-demo.cc: // Description: //% Catalan (step-)RGS for lattice paths from (0,0) to (n,n) //% that do not go below the diagonal (k, k) for 0 <= k <= n. //% Lexicographic order. //% Cf. OEIS sequence A000108. arg 1: 5 == n [Catalan (step-)RGS for paths from (0,0) to (n,n)] default=5 arg 2: 0 == pq [Whether do draw path (as ASCII art)] default=0 1: [ . . . . . ] 0 ((((())))) 2: [ . . . . 1 ] 4 (((()()))) 3: [ . . . . 2 ] 4 (((())())) 4: [ . . . . 3 ] 4 (((()))()) 5: [ . . . . 4 ] 4 (((())))() 6: [ . . . 1 1 ] 3 ((()(()))) 7: [ . . . 1 2 ] 4 ((()()())) 8: [ . . . 1 3 ] 4 ((()())()) 9: [ . . . 1 4 ] 4 ((()()))() 10: [ . . . 2 2 ] 3 ((())(())) 11: [ . . . 2 3 ] 4 ((())()()) 12: [ . . . 2 4 ] 4 ((())())() 13: [ . . . 3 3 ] 3 ((()))(()) 14: [ . . . 3 4 ] 4 ((()))()() 15: [ . . 1 1 1 ] 2 (()((()))) 16: [ . . 1 1 2 ] 4 (()(()())) 17: [ . . 1 1 3 ] 4 (()(())()) 18: [ . . 1 1 4 ] 4 (()(()))() 19: [ . . 1 2 2 ] 3 (()()(())) 20: [ . . 1 2 3 ] 4 (()()()()) 21: [ . . 1 2 4 ] 4 (()()())() 22: [ . . 1 3 3 ] 3 (()())(()) 23: [ . . 1 3 4 ] 4 (()())()() 24: [ . . 2 2 2 ] 2 (())((())) 25: [ . . 2 2 3 ] 4 (())(()()) 26: [ . . 2 2 4 ] 4 (())(())() 27: [ . . 2 3 3 ] 3 (())()(()) 28: [ . . 2 3 4 ] 4 (())()()() 29: [ . 1 1 1 1 ] 1 ()(((()))) 30: [ . 1 1 1 2 ] 4 ()((()())) 31: [ . 1 1 1 3 ] 4 ()((())()) 32: [ . 1 1 1 4 ] 4 ()((()))() 33: [ . 1 1 2 2 ] 3 ()(()(())) 34: [ . 1 1 2 3 ] 4 ()(()()()) 35: [ . 1 1 2 4 ] 4 ()(()())() 36: [ . 1 1 3 3 ] 3 ()(())(()) 37: [ . 1 1 3 4 ] 4 ()(())()() 38: [ . 1 2 2 2 ] 2 ()()((())) 39: [ . 1 2 2 3 ] 4 ()()(()()) 40: [ . 1 2 2 4 ] 4 ()()(())() 41: [ . 1 2 3 3 ] 3 ()()()(()) 42: [ . 1 2 3 4 ] 4 ()()()()() ct=42