A280844 Number of 2 X 2 matrices with entries in {-n,..,0,..,n} with no entries repeated having permanent = trace^n.

0, 0, 0, 4, 16, 20, 16, 36, 56, 60, 72, 76, 80, 100, 112, 100, 136, 124, 152, 172, 192, 196, 224, 196, 232, 236, 264, 252, 288, 276, 288, 308, 344, 332, 344, 332, 384, 388, 416, 404, 456, 428, 456, 444, 496, 468, 512, 468, 536, 556, 648

Offset

0,4

Comments

a(n) is also equal to the number of 2 X 2 matrices with entries in {-n,..,0,..n} with no elements repeated having determinant = trace^n except a(4). For permanent = trace^n, a(4) = 16 but for determinant = trace^n, a(4) = 24.

a(n) mod 4 = 0.

Links

Indranil Ghosh, Table of n, a(n) for n = 0..103

Example

For n = 5, the possible matrices are [-3,-5,-1,2], [-3,-1,-5,2],
[-3,1,5,2], [-3,5,1,2], [-2,-4,-1,2], [-2,-1,-4,2], [-2,1,4,2], [-2,4,1,2], [-1,1,3,2], [-1,3,1,2], [2,-5,-1,-3], [2,-4,-1,-2],
[2,-1,-5,-3], [2,-1,-4,-2], [2,1,3,-1], [2,1,4,-2], [2,1,5,-3],
[2,3,1,-1], [2,4,1,-2] and [2,5,1,-3].
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]. There are 20 possibilities. So, for n = 5, a(n) = 20.

Prog

(Python)
def t(n):
    s=0
    for a in range(-n, n+1):
        for b in range(-n, n+1):
            if a!=b:
                for c in range(-n, n+1):
                    if a!=c and b!=c:
                        for d in range(-n, n+1):
                            if d!=a and d!=b and d!=c:
                                if (a*d+b*c)==(a+d)**n:
                                    s+=1
    return s
for i in range(0, 104):
    print str(i)+" "+str(t(i))

Crossrefs

Cf. A278933, A278902, A279018.

Sequence in context: A232524 A032827 A328465 * A277887 A216033 A071966

Adjacent sequences: A280841 A280842 A280843 * A280845 A280846 A280847

Keyword

nonn

Author

Indranil Ghosh, Jan 09 2017

Status

approved