Buggy python submission (verdict: Time Limit Exceeded):
from sys import exit, setrecursionlimit, stderr
from functools import reduce
from itertools import *
from collections import defaultdict, Counter
from bisect import bisect

def read():
  return int(input())

def reads():
  return [int(x) for x in input().split()]

H, W = reads()
S = []
for _ in range(H):
  S.append(input())

N = H + W
field = [[0] * N for _ in range(N)]
for i in range(H):
  for j in range(W):
    field[i+j][i-j+W] = int(S[i][j] == '#')

accRow = [None] * N
for i in range(N):
  accRow[i] = [0] + list(accumulate(field[i][j] for j in range(N)))

accCol = [None] * N
for i in range(N):
  accCol[i] = [0] + list(accumulate(field[j][i] for j in range(N)))

# for f in field:
#   print(f)

ans = 0
for i in range(N):
  for j in range((i+W)%2, N, 2):
    for k in range(j+2, N, 2):
      d = k - j
      if field[i][j] == field[i][k] == 1:
        if i - d >= 0:
          ans += accRow[i-d][k+1] - accRow[i-d][j]
        if i + d < N:
          ans += accRow[i+d][k+1] - accRow[i+d][j]
      if field[j][i] == field[k][i] == 1:
        if i - d >= 0:
          ans += accCol[i-d][k+1] - accCol[i-d][j]
        if i + d < N:
          ans += accCol[i+d][k+1] - accCol[i+d][j]

for i in range(N):
  for j in range((i+W)%2, N, 2):
    if field[i][j] != 1:
      continue
    for d in range(2, N, 2):
      if i + d < N and j + d < N and field[i][j+d] == field[i+d][j] == 1:
        ans -= 1
      if i + d < N and j - d >= 0 and field[i][j-d] == field[i+d][j] == 1:
        ans -= 1
      if i - d >= 0 and j - d >= 0 and field[i][j-d] == field[i-d][j] == 1:
        ans -= 1
      if i - d >= 0 and j + d < N and field[i][j+d] == field[i-d][j] == 1:
        ans -= 1

print(ans)

Fixed submission:
from sys import exit, setrecursionlimit, stderr
from functools import reduce
from itertools import *
from collections import defaultdict, Counter
from bisect import bisect

def read():
  return int(input())

def reads():
  return [int(x) for x in input().split()]

H, W = reads()
S = []
for _ in range(H):
  S.append(input())

N = H + W
field = [[0] * N for _ in range(N)]
for i in range(H):
  for j in range(W):
    field[i+j][i-j+W] = int(S[i][j] == '#')

accRow = [None] * N
for i in range(N):
  accRow[i] = [0] + list(accumulate(field[i][j] for j in range(N)))

accCol = [None] * N
for i in range(N):
  accCol[i] = [0] + list(accumulate(field[j][i] for j in range(N)))

# for f in field:
#   print(f)

ans = 0
for i in range(N):
  for j in range((i+W)%2, N, 2):
    for k in range(j+2, N, 2):
      d = k - j
      if field[i][j] == field[i][k] == 1:
        if i - d >= 0:
          ans += accRow[i-d][k+1] - accRow[i-d][j]
        if i + d < N:
          ans += accRow[i+d][k+1] - accRow[i+d][j]
      if field[j][i] == field[k][i] == 1:
        if i - d >= 0:
          ans += accCol[i-d][k] - accCol[i-d][j+1]
        if i + d < N:
          ans += accCol[i+d][k] - accCol[i+d][j+1]

print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
from sys import exit, setrecursionlimit, stderr
from functools import reduce
from itertools import *
from collections import defaultdict, Counter
from bisect import bisect

def read():
  return int(input())

def reads():
  return [int(x) for x in input().split()]

H, W = reads()
S = []
for _ in range(H):
  S.append(input())

N = H + W
field = [[0] * N for _ in range(N)]
for i in range(H):
  for j in range(W):
    field[i+j][i-j+W] = int(S[i][j] == '#')

accRow = [None] * N
for i in range(N):
  accRow[i] = [0] + list(accumulate(field[i][j] for j in range(N)))

accCol = [None] * N
for i in range(N):
  accCol[i] = [0] + list(accumulate(field[j][i] for j in range(N)))

ans = 0
for i in range(N):
  for j in range(N):
    for k in range(j+1, N):
      d = k - j
      if field[i][j] == field[i][k] == 1:
        if i - d >= 0:
          ans += accRow[i-d][k+1] - accRow[i-d][j]
        if i + d < N:
          ans += accRow[i+d][k+1] - accRow[i+d][j]
      if field[j][i] == field[k][i] == 1:
        if i - d >= 0:
          ans += accCol[i-d][k+1] - accCol[i-d][j]
        if i + d < N:
          ans += accCol[i+d][k+1] - accCol[i+d][j]

for i in range(N):
  for j in range(N):
    if field[i][j] != 1:
      continue
    for d in range(1, N):
      if i + d < N and j + d < N and field[i][j+d] == field[i+d][j] == 1:
        ans -= 1
      if i + d < N and j - d >= 0 and field[i][j-d] == field[i+d][j] == 1:
        ans -= 1
      if i - d >= 0 and j - d >= 0 and field[i][j-d] == field[i-d][j] == 1:
        ans -= 1
      if i - d >= 0 and j + d < N and field[i][j+d] == field[i-d][j] == 1:
        ans -= 1

print(ans)

Fixed submission:
from sys import exit, setrecursionlimit, stderr
from functools import reduce
from itertools import *
from collections import defaultdict, Counter
from bisect import bisect

def read():
  return int(input())

def reads():
  return [int(x) for x in input().split()]

H, W = reads()
S = []
for _ in range(H):
  S.append(input())

N = H + W
field = [[0] * N for _ in range(N)]
for i in range(H):
  for j in range(W):
    field[i+j][i-j+W] = int(S[i][j] == '#')

accRow = [None] * N
for i in range(N):
  accRow[i] = [0] + list(accumulate(field[i][j] for j in range(N)))

accCol = [None] * N
for i in range(N):
  accCol[i] = [0] + list(accumulate(field[j][i] for j in range(N)))

# for f in field:
#   print(f)

ans = 0
for i in range(N):
  for j in range((i+W)%2, N, 2):
    for k in range(j+2, N, 2):
      d = k - j
      if field[i][j] == field[i][k] == 1:
        if i - d >= 0:
          ans += accRow[i-d][k+1] - accRow[i-d][j]
        if i + d < N:
          ans += accRow[i+d][k+1] - accRow[i+d][j]
      if field[j][i] == field[k][i] == 1:
        if i - d >= 0:
          ans += accCol[i-d][k] - accCol[i-d][j+1]
        if i + d < N:
          ans += accCol[i+d][k] - accCol[i+d][j+1]

print(ans)