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A280407
Number of 2 X 2 matrices with all elements in {-n,..,0,..,n} with permanent = determinant * n.
1
1, 45, 81, 233, 289, 601, 625, 1113, 1153, 1785, 1681, 2761, 2401, 3577, 3505, 4665, 4225, 6185, 5329, 7673, 6945, 8601, 7921, 11033, 9665, 12265, 11793, 14089, 12769, 18073, 14641, 19945, 17281, 20121, 20593, 23961, 21025, 25417, 24177, 29177, 25921, 35449, 28561, 36233
OFFSET
0,2
LINKS
EXAMPLE
For n = 2, few of the possible matrices are [-2,-2,0,0], [-2,-1,0,0], [-2,0,-2,0], [-2,0,-1,0], [-2,0,0,0], [-2,0,1,0], [-2,0,2,0], [1,0,0,0], [1,0,1,0], [1,0,2,0], [1,1,0,0], [1,2,0,0], [2,-2,0,0], [2,-1,0,0], [2,0,-2,0], .... There are 81 possibilities. Here each of the matrices is defined as M = [a,b,c,d] where a = M[1][1], b = M[1][2], c = M[2][1], d = M[2][2]. So for n = 2, a(n)=81.
PROG
(Python)
def t(n):
s=0
for a in range(-n, n+1):
for b in range(-n, n+1):
for c in range(-n, n+1):
for d in range(-n, n+1):
if (a*d-b*c)*n==(a*d+b*c):
s+=1
return s
for i in range(0, 156):
print str(i)+" "+str(t(i))
CROSSREFS
Number of 2 X 2 matrices with all elements in {0,..,n}: A280391 (permanent = determinant * n), A280321 (determinant = permanent * n), A015237 (determinant = permanent) and A016754 (determinant = 2* permanent).
Sequence in context: A026060 A138171 A305154 * A063343 A043184 A039361
KEYWORD
nonn
AUTHOR
Indranil Ghosh, Jan 06 2017
STATUS
approved