euler114.py

#-3= -1-2 for 1,2 don't count
#+1 = none at all scenario
import math
n=50
sum1=((n*(n-2))/8)+1
print sum1
sum = 0
for i in range(3, int(n/2)):
    print "i:",i
    for k in range(2, int(n/i)+1):#one block of three, two blocks, etc
        print "k:",k
        slots = k+1
        stones = n-(i*k)-(k-1)
        if(slots-stones >= 0 and stones>=0):
            sum += math.factorial(slots)/(math.factorial(slots-stones)*math.factorial(stones))
        elif(slots==stones):
            sum+=1
print sum+sum1