# This file was *autogenerated* from the file counts.sage.
from sage.all_cmdline import *
def count_sum(max, total, dice):
    count = Integer(0)
    if total < Integer(1) or total > max*dice:
        return Integer(0)
    if dice == Integer(1):
        if Integer(1) <= total <= max:
            return Integer(1)
        else:
            return Integer(0)
    for last in range(Integer(1), max+Integer(1)):
        count += count_sum(max, total-last, dice-Integer(1))
    return count

v = [count_sum(Integer(10),k,Integer(3)) for k in range(Integer(32))]
print v
t = sum([a*a for a in v])
print t, t/Integer(13)


def delta(x,y):
    return Integer(1) if x==y else Integer(0)

vv = [Integer(0)]*Integer(31)
ww = [Integer(0)]*Integer(31)
for i in range(Integer(10)):
        for j in range(Integer(10)):
            for k in range(Integer(10)):
                total = i+j+k
                vv[total] += Integer(1)
                if i != Integer(0):
                    ww[total] += Integer(1)

print vv
print ww

t = sum([a*b for a,b in zip(vv, ww)])
print t, t/Integer(13)

t = sum([a*a for a in vv])
print t, t/Integer(13)