In [1]:

    

def memofibo(n):
    chart = {}
    chart[1] = 1
    chart[2] = 1
    for n in range(3,n+1):
        chart[n] = chart[n-2] + chart[n-1]
    return chart


    

In [2]:

    

memofibo(100)


    

    
Out[2]:





{1: 1,
 2: 1,
 3: 2,
 4: 3,
 5: 5,
 6: 8,
 7: 13,
 8: 21,
 9: 34,
 10: 55,
 11: 89,
 12: 144,
 13: 233,
 14: 377,
 15: 610,
 16: 987,
 17: 1597,
 18: 2584,
 19: 4181,
 20: 6765,
 21: 10946,
 22: 17711,
 23: 28657,
 24: 46368,
 25: 75025,
 26: 121393,
 27: 196418,
 28: 317811,
 29: 514229,
 30: 832040,
 31: 1346269,
 32: 2178309,
 33: 3524578,
 34: 5702887,
 35: 9227465,
 36: 14930352,
 37: 24157817,
 38: 39088169,
 39: 63245986,
 40: 102334155,
 41: 165580141,
 42: 267914296,
 43: 433494437,
 44: 701408733,
 45: 1134903170,
 46: 1836311903,
 47: 2971215073,
 48: 4807526976,
 49: 7778742049,
 50: 12586269025,
 51: 20365011074,
 52: 32951280099,
 53: 53316291173,
 54: 86267571272,
 55: 139583862445,
 56: 225851433717,
 57: 365435296162,
 58: 591286729879,
 59: 956722026041,
 60: 1548008755920,
 61: 2504730781961,
 62: 4052739537881,
 63: 6557470319842,
 64: 10610209857723,
 65: 17167680177565,
 66: 27777890035288,
 67: 44945570212853,
 68: 72723460248141,
 69: 117669030460994,
 70: 190392490709135,
 71: 308061521170129,
 72: 498454011879264,
 73: 806515533049393,
 74: 1304969544928657,
 75: 2111485077978050,
 76: 3416454622906707,
 77: 5527939700884757,
 78: 8944394323791464,
 79: 14472334024676221,
 80: 23416728348467685,
 81: 37889062373143906,
 82: 61305790721611591,
 83: 99194853094755497,
 84: 160500643816367088,
 85: 259695496911122585,
 86: 420196140727489673,
 87: 679891637638612258,
 88: 1100087778366101931,
 89: 1779979416004714189,
 90: 2880067194370816120,
 91: 4660046610375530309,
 92: 7540113804746346429,
 93: 12200160415121876738,
 94: 19740274219868223167,
 95: 31940434634990099905,
 96: 51680708854858323072,
 97: 83621143489848422977,
 98: 135301852344706746049,
 99: 218922995834555169026,
 100: 354224848179261915075}

In [3]:

    

memofibo(20)


    

    
Out[3]:





{1: 1,
 2: 1,
 3: 2,
 4: 3,
 5: 5,
 6: 8,
 7: 13,
 8: 21,
 9: 34,
 10: 55,
 11: 89,
 12: 144,
 13: 233,
 14: 377,
 15: 610,
 16: 987,
 17: 1597,
 18: 2584,
 19: 4181,
 20: 6765}

In [4]:

    

from sympy import init_session


    

In [5]:

    

init_session(quiet=True)


    

    




IPython console for SymPy 1.0 (Python 3.5.2-64-bit) (ground types: python)

In [6]:

    

Integral(sqrt(1/x), x)


    

    
Out[6]:





$$\int \sqrt{\frac{1}{x}}\, dx$$

In [7]:

    

Integral((x**(1/y)), (x, 1, oo), (y, 1, oo))


    

    
Out[7]:





$$\int_{1}^{\infty}\int_{1}^{\infty} x^{\frac{1}{y}}\, dx\, dy$$

In [8]:

    

Integral(x**x, (x, 0, 1))


    

    
Out[8]:





$$\int_{0}^{1} x^{x}\, dx$$

In [ ]: