def T(n):
ntmax = n / 2
tot = 0
for i in xrange(ntmax):
opentiles = n - i * 2
c = nCr(n, opentiles)
tot += c
print n, i, opentiles, c, 10**opentiles
return tot
def T(n):
ntmax = n/2
tot = 0
for i in xrange(ntmax):
opentiles = n - i*2
c = nCr(n,opentiles)
tot +=c
print n,i,opentiles, c, 10**opentiles
return tot
def Lucas(N,k,p):
s1 = b10Tobm(N,p)
s2 = b10Tobm(k,p)
l = len(s1)
if l>len(s2):
sa = [0]*(l-len(s2))
s2 = sa + s2
v = 1
for i in xrange(l):
a = int(s1[i])
b = int(s2[i])
v *= nCr(a,b)
v %= p
return v
from Functions import nCr
summ = 0
for i in xrange(14):
z = 2 * (i + 2) * (i + 1) * 16**i
summ += z
print z
print summ
summ2 = 0
for i in xrange(13):
#z = 13*(i+3)*(i+2)*(i+1)*16**i
z = 16 * nCr(i + 3, 3) * 16**i
summ2 += z
print z
print
print summ2
summ3 = 0
for k in xrange(3, 17):
summ3 += 15 * 16**(k - 1) - 15**(k) - (2 * 14) * 15**(k - 1) + (
13 * 14**(k - 1)) + 2 * 14**k - 13**k
# for i in xrange(3,17):
# summ2 +=43 * 15**(i - 1)* 13**i
# print
def R(n, m, k):
return nCr(n, k) * subFactorial(m - k)
def subFactorial(n):
summ = 0
for x in xrange(n + 1):
summ += float(pow(-1, x)) / factorial(x)
return factorial(n) * summ
def R(n, m, k):
return nCr(n, k) * subFactorial(m - k)
st = time()
z = 0.0
fixed = nCr(25, 3)
fact100 = factorial(100)
for k in xrange(23):
z += R(75, 97, k) * fixed / fact100
print "Probability is ", z
print "time elapsed ", time() - st
# for m in xrange(1,7):
# print R(8,m)
# print R(25,22)
# print R(25,3)/factorial(25)
# print
#
#
#
#
#
from math import ceil
from Functions import nCr,RetFact
from time import time
st = time()
sf = {}
for r in xrange(0, 51):
for c in xrange(1,int(ceil(r/2))+1):
v = nCr(r,c)
if v in sf: continue
facts = RetFact(v)
setfacts = set(facts)
if len(facts)>len(setfacts): continue
sf[v]=v
print
#print sf
#print
print 1 + sum(sf)
print time()-st
def R(n,m,k): return nCr(n,k)*subFactorial(m-k)
from Functions import nCr
from math import factorial
from time import time
def subFactorial(n):
summ = 0
for x in xrange(n+1): summ += float(pow(-1,x))/factorial(x)
return factorial(n) * summ
def R(n,m,k):
return nCr(n,k)*subFactorial(m-k)
st =time()
z = 0.0
fixed = nCr(25, 3)
fact100 = factorial(100)
for k in xrange(23):z += R(75,97,k) * fixed / fact100
print "Probability is ", z
print "time elapsed ", time()-st
# for m in xrange(1,7):
# print R(8,m)
# print R(25,22)
# print R(25,3)/factorial(25)
# print
# for i in xrange(25,101):
from Functions import nCr summ = 0 for i in xrange(14): z = 2*(i+2)*(i+1)*16**i summ += z print z print summ summ2 =0 for i in xrange(13): #z = 13*(i+3)*(i+2)*(i+1)*16**i z = 16*nCr(i+3,3)*16**i summ2 += z print z print print summ2 summ3=0 for k in xrange(3,17): summ3+=15*16**(k-1)-15**(k)-(2*14)*15**(k-1)+(13*14**(k-1))+2*14**k-13**k # for i in xrange(3,17): # summ2 +=43 * 15**(i - 1)* 13**i # print # summ -=summ2
from Functions import nCr
ctr = 0
for i in xrange(7, 200):
print i, ";",
ctr2 = 0
if i % 2 == 1:
dbl = True
rng = int(i / 2.)
else:
dble = False
rng = int(i / 2.)
for j in xrange(1, rng + 1):
#print nCr(i,j),
x = nCr(i, j)
if x % 7 == 0:
#ctr +=1
ctr2 += 1
# print x
if dbl:
ctr2 *= 2
else:
ctr2 = ctr * 2
ctr += ctr2
print "***** ", i, ctr2
print
print
print ctr
ctr=0
for i in xrange(7,200):
print i,";",
ctr2=0
if i%2==1:
dbl = True
rng = int(i/2.)
else:
dble = False
rng = int(i/2.)
for j in xrange(1,rng+1):
#print nCr(i,j),
x=nCr(i,j)
if x%7==0:
#ctr +=1
ctr2 +=1
# print x
if dbl:
ctr2 *=2
else:
ctr2 =ctr*2
ctr += ctr2
print "***** ",i,ctr2
print
print
print ctr
def R(n,k): return nCr(n,k)*subFactorial(n-k)
summ += float(pow(-1,x))/factorial(x)
return factorial(n) * summ
st =time()
def R(n,k):
return nCr(n,k)*subFactorial(n-k)
z = 0.0
for k in xrange(23):
#z += (-1.0)**k * nCr(22, k) * factorial(97 - k) * nCr(25, 3) / factorial(100)
z += nCr(75,k) * subFactorial(97 - k) * nCr(25, 3) / factorial(100)
#z = sum((-1.0)**k * nCr(22, k) * factorial(97 - k) for k in range(23)) * nCr(25, 3) / factorial(100)
print z
# for m in xrange(1,7):
# print R(8,m)
# print R(25,22)
# print R(25,3)/factorial(25)
# print
# for i in xrange(25,101):
# for j in xrange(3,79):
# if j> i:continue
def R(n, k):
return nCr(n, k) * subFactorial(n - k)
return factorial(n) * summ
st = time()
def R(n, k):
return nCr(n, k) * subFactorial(n - k)
z = 0.0
for k in xrange(23):
#z += (-1.0)**k * nCr(22, k) * factorial(97 - k) * nCr(25, 3) / factorial(100)
z += nCr(75, k) * subFactorial(97 - k) * nCr(25, 3) / factorial(100)
#z = sum((-1.0)**k * nCr(22, k) * factorial(97 - k) for k in range(23)) * nCr(25, 3) / factorial(100)
print z
# for m in xrange(1,7):
# print R(8,m)
# print R(25,22)
# print R(25,3)/factorial(25)
# print
# for i in xrange(25,101):
# for j in xrange(3,79):
# if j> i:continue