login
A276113
Number of 2 X 2 matrices with entries in {0,1,...,n} and permanent = (trace)^2 with no entry repeated.
1
0, 0, 0, 0, 4, 4, 4, 8, 12, 24, 24, 24, 32, 52, 56, 56, 76, 76, 88, 120, 124, 152, 152, 152, 160, 192, 212, 236, 288, 288, 288, 352, 372, 372, 372, 376, 420, 496, 528, 600, 604, 604, 632, 724, 728, 740, 740, 740, 788, 932, 964
OFFSET
0,5
COMMENTS
All terms are multiples of 4 since the diagonals can be permuted. - Charles R Greathouse IV, Dec 12 2016
LINKS
Indranil Ghosh and Charles R Greathouse IV, Table of n, a(n) for n = 0..5000 (terms up to 200 from Indranil Ghosh)
PROG
(Python)
def t(n):
s=0
for a in range(n+1):
for b in range(n+1):
for c in range(n+1):
for d in range(n+1):
if (a!=b and a!=d and b!=d and c!=a and c!=b and c!=d):
if a*d+b*c==(a+d)**2:
s+=1
return s
for i in range(201):
print(str(i)+" "+str(t(i)))
(PARI) a(n)=my(n2=n^2); 4*sum(a=0, n, sum(d=a+1, n, my(t=(a+d)^2-a*d, c); if(t>0 && t<n2, sumdiv(t, b, b^2<t && a!=b && b!=d && (c=t/b)<=n && a!=c && c!=d), 0))) \\ Charles R Greathouse IV, Dec 12 2016
CROSSREFS
Cf. A210289.
Sequence in context: A110757 A377468 A167184 * A232406 A322040 A085071
KEYWORD
nonn
AUTHOR
Indranil Ghosh, Dec 11 2016
STATUS
approved