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EXAMPLE
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The sequence together with the corresponding compositions begins:
0: () 45: (2,1,2,1) 86: (2,2,1,2)
2: (2) 46: (2,1,1,2) 87: (2,2,1,1,1)
4: (3) 53: (1,2,2,1) 88: (2,1,4)
8: (4) 54: (1,2,1,2) 90: (2,1,2,2)
10: (2,2) 58: (1,1,2,2) 91: (2,1,2,1,1)
16: (5) 64: (7) 93: (2,1,1,2,1)
21: (2,2,1) 69: (4,2,1) 94: (2,1,1,1,2)
22: (2,1,2) 70: (4,1,2) 98: (1,4,2)
26: (1,2,2) 73: (3,3,1) 100: (1,3,3)
32: (6) 74: (3,2,2) 104: (1,2,4)
34: (4,2) 76: (3,1,3) 106: (1,2,2,2)
36: (3,3) 81: (2,4,1) 107: (1,2,2,1,1)
40: (2,4) 82: (2,3,2) 109: (1,2,1,2,1)
42: (2,2,2) 84: (2,2,3) 110: (1,2,1,1,2)
43: (2,2,1,1) 85: (2,2,2,1) 117: (1,1,2,2,1)
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