import matplotlib.pyplot as plt

def a(k,n) :
    if k == 1 :
        return 2**(-n)
    elif k == 2 :
        return n**(-1/2)
    elif k == 3 :
        return n**(-2)
    elif k == 4 :
        return 1
        
def f(k,p) :
    L = [1,a(k,1)]
    if p == 0 :
        return L[0]
    else :
        for n in range(2,p+1) :
            L.append(a(k,n)*L[-1]+L[-2])
        return L

def S(k,p) :
    L = f(k,p)
    return [(-1)**k/(L[k]*L[k-1]) for k in range(1,p+1)]

k = 4   
N = list(range(1,21))
plt.plot(N,S(k,20))
plt.show()