python3 - <<'PY'
from itertools import product
M=lambda x:x-7*(x//7)
o=0
for a,b,c,d,e,f in product(range(7),repeat=6):
 h=M(a*a-a*b+b*b)
 R=M(c*c+d*d+e*e+f*f)
 if h and (a or b) and (c or d or e or f) and M(3*h-2*R)==0 and M(c*d+e*f)==0:
  o+=1
print(o//12)
PY