Sum of Ones in Matrix 2^n by 2^(n+1)

sum_of_matrix.py

import numpy as np
def sum_of_bins_greater_then(n):
  print("n =",n)
  left = []
  for i in range(2**n):
    left += [sum(int(x) for x in bin(i)[2:])]
  up = []
  for i in range(2**(n+1)):
    up += [sum(int(x) for x in bin(i)[2:])]
  print("Matrix shape", len(left),'x',len(up))
  m = np.zeros((2**n, 2**(n+1)))-1
  for li, l in enumerate(left):
    # print('')
    for ui, u in enumerate(up):
      m[li,ui]=int(l<u)
      # print(f"{0:1}", int(m[li,ui]), end=' ')
  twopowertwoN = 2**(2*n)
  print('2^(2*n)=', twopowertwoN)
  print('Matrix sum', int(np.sum(m)))
  print("Equals?",twopowertwoN==np.sum(m))
  print('')

# Main Run ~5 minutes
for i in range(15):
  sum_of_bins_greater_then(i)

"""
OUTPUT
n = 0
Matrix shape 1 x 2
2^(2*n)= 1
Matrix sum 1
Equals? True

n = 1
Matrix shape 2 x 4
2^(2*n)= 4
Matrix sum 4
Equals? True

n = 2
Matrix shape 4 x 8
2^(2*n)= 16
Matrix sum 16
Equals? True

n = 3
Matrix shape 8 x 16
2^(2*n)= 64
Matrix sum 64
Equals? True

n = 4
Matrix shape 16 x 32
2^(2*n)= 256
Matrix sum 256
Equals? True

n = 5
Matrix shape 32 x 64
2^(2*n)= 1024
Matrix sum 1024
Equals? True

n = 6
Matrix shape 64 x 128
2^(2*n)= 4096
Matrix sum 4096
Equals? True

n = 7
Matrix shape 128 x 256
2^(2*n)= 16384
Matrix sum 16384
Equals? True

n = 8
Matrix shape 256 x 512
2^(2*n)= 65536
Matrix sum 65536
Equals? True

n = 9
Matrix shape 512 x 1024
2^(2*n)= 262144
Matrix sum 262144
Equals? True

n = 10
Matrix shape 1024 x 2048
2^(2*n)= 1048576
Matrix sum 1048576
Equals? True

n = 11
Matrix shape 2048 x 4096
2^(2*n)= 4194304
Matrix sum 4194304
Equals? True

n = 12
Matrix shape 4096 x 8192
2^(2*n)= 16777216
Matrix sum 16777216
Equals? True

n = 13
Matrix shape 8192 x 16384
2^(2*n)= 67108864
Matrix sum 67108864
Equals? True

n = 14
Matrix shape 16384 x 32768
2^(2*n)= 268435456
Matrix sum 268435456
Equals? True
"""