def expand(n):
#expanding (9 + 4sqrt(5))^n into rational and irrational part
#rational part
rat_res = 0
irrat_res = 0
for k in range(0, n + 1, 2):
rat_res += nChoosek(n, k) * 9**(n-k) * 4**k * 5**(k//2)
for k in range(1, n + 1, 2):
irrat_res += nChoosek(n, k) * 9**(n-k) * 4**k * 5**((k-1)//2)
return rat_res, irrat_res
def expand(n):
#expanding (a + bsqrt(c))^n into rational and irrational part
#rational part
a = 9
b = 4
c = 5
rat_res = 0
irrat_res = 0
for k in range(0, n + 1, 2):
rat_res += nChoosek(n, k) * a**(n - k) * b**k * c**(k // 2)
for k in range(1, n + 1, 2):
irrat_res += nChoosek(n, k) * a**(n - k) * b**k * c**((k - 1) // 2)
return rat_res, irrat_res
def count_incr(exp_10):
return nChoosek(10 + exp_10 - 1, exp_10)
# -*- coding: utf-8 -*-
"""For any subset pairs of size i there are n choose 2i ways to choose the 2i
members, and (2i-1) choose (i-2) ways to distribute the members of
"""
from eulerTools import nChoosek
from datetime import datetime
startTime = datetime.now()
n = 12
resSum = 0
for i in range(2, n // 2 + 1):
resSum += nChoosek(n, 2 * i) * nChoosek(2 * i - 1, i - 2)
print("result = " + str(resSum))
print(datetime.now() - startTime)
def square_calc(l, w):
if l == 0 or w == 0:
return 0
return nChoosek(l + 1, 2) * nChoosek(w + 1, 2)
return 0
return nChoosek(l + 1, 2) * nChoosek(w + 1, 2)
startTime = datetime.now()
start = timer()
square_arr = [0 for i in range(44)]
hard_square_arr = [0 for i in range(44)]
for idx in range(2, 44):
count = 0
length = 2 * (idx - 1)
width = 2
while length > width:
count += 2 * nChoosek(length + 1, 2) * nChoosek(width + 1, 2)
length -= 2
width += 2
if length == width:
count += nChoosek(length + 1, 2)**2
hard_square_arr[idx] = count
count -= hard_square_arr[idx - 1]
square_arr[idx] = count
res = 0
for a in range(43 + 1):
res += square_arr[a]
res += square_calc(a, a)
base_count = 0
for x in range(1, 2 * a):