> perl ch-2.pl

n = 1 => 1 ways:
        [1]
n = 2 => 2 ways:
        [1 1]
        [2]
n = 3 => 3 ways:
        [1 1]
        [1 1 2]
        [2 2]
n = 4 => 3 ways:
        [1 1 1]
        [2 1]
        [1 2]
n = 5 => 5 ways:
        [1 1 1]
        [1 1 2 1]
        [2 2 1]
        [1 1 2]
        [2 2]
Switching to count only method, omitting the sequences...
n = 6 => 13 ways
n = 7 => 21 ways
n = 8 => 34 ways
n = 9 => 55 ways
n = 10 => 89 ways
n = 11 => 144 ways
n = 12 => 233 ways
n = 13 => 377 ways
n = 14 => 610 ways
n = 15 => 987 ways
n = 16 => 1597 ways
n = 17 => 2584 ways
n = 18 => 4181 ways
n = 19 => 6765 ways
n = 20 => 10946 ways
n = 21 => 17711 ways
n = 22 => 28657 ways
n = 23 => 46368 ways
n = 24 => 75025 ways
n = 25 => 121393 ways
n = 26 => 196418 ways
n = 27 => 317811 ways
n = 28 => 514229 ways
n = 29 => 832040 ways
n = 30 => 1346269 ways
n = 31 => 2178309 ways
n = 32 => 3524578 ways
n = 33 => 5702887 ways
n = 34 => 9227465 ways
n = 35 => 14930352 ways
n = 36 => 24157817 ways
n = 37 => 39088169 ways
n = 38 => 63245986 ways
n = 39 => 102334155 ways
n = 40 => 165580141 ways
n = 41 => 267914296 ways
n = 42 => 433494437 ways
n = 43 => 701408733 ways
n = 44 => 1134903170 ways
n = 45 => 1836311903 ways
n = 46 => 2971215073 ways
n = 47 => 4807526976 ways
n = 48 => 7778742049 ways
n = 49 => 12586269025 ways
n = 50 => 20365011074 ways
n = 51 => 32951280099 ways
n = 52 => 53316291173 ways
n = 53 => 86267571272 ways
n = 54 => 139583862445 ways
n = 55 => 225851433717 ways
n = 56 => 365435296162 ways
n = 57 => 591286729879 ways
n = 58 => 956722026041 ways
n = 59 => 1548008755920 ways
n = 60 => 2504730781961 ways
n = 61 => 4052739537881 ways
n = 62 => 6557470319842 ways
n = 63 => 10610209857723 ways
n = 64 => 17167680177565 ways
n = 65 => 27777890035288 ways
n = 66 => 44945570212853 ways
n = 67 => 72723460248141 ways
n = 68 => 117669030460994 ways
n = 69 => 190392490709135 ways
n = 70 => 308061521170129 ways
n = 71 => 498454011879264 ways
n = 72 => 806515533049393 ways
n = 73 => 1304969544928657 ways
n = 74 => 2111485077978050 ways
n = 75 => 3416454622906707 ways
n = 76 => 5527939700884757 ways
n = 77 => 8944394323791464 ways
n = 78 => 14472334024676221 ways
n = 79 => 23416728348467685 ways
n = 80 => 37889062373143906 ways
n = 81 => 61305790721611591 ways
n = 82 => 99194853094755497 ways
n = 83 => 160500643816367088 ways
n = 84 => 259695496911122585 ways
n = 85 => 420196140727489673 ways
n = 86 => 679891637638612258 ways
n = 87 => 1100087778366101931 ways
n = 88 => 1779979416004714189 ways
n = 89 => 2880067194370816120 ways
n = 90 => 4660046610375530309 ways
n = 91 => 7540113804746346429 ways
n = 92 => 12200160415121876738 ways
n = 93 => 1.97402742198682e+19 ways
n = 94 => 3.19404346349901e+19 ways
n = 95 => 5.16807088548583e+19 ways
n = 96 => 8.36211434898484e+19 ways
n = 97 => 1.35301852344707e+20 ways
n = 98 => 2.18922995834555e+20 ways
n = 99 => 3.54224848179262e+20 ways
n = 100 => 5.73147844013817e+20 ways