A280588 Number of 2 X 2 matrices with all terms in {0,1,...,n} and (sum of terms) = determinant.

1, 1, 2, 9, 18, 41, 58, 97, 130, 185, 226, 313, 354, 457, 538, 649, 738, 889, 954, 1145, 1266, 1449, 1578, 1809, 1930, 2177, 2362, 2609, 2770, 3129, 3242, 3609, 3810, 4097, 4402, 4793, 5026, 5433, 5674, 6097, 6346, 6929, 7090, 7641, 8010, 8433, 8810, 9369, 9626, 10297, 10690

Offset

0,3

Links

Indranil Ghosh and Chai Wah Wu, Table of n, a(n) for n = 0..10000 (terms for n = 0..200 from Indranil Ghosh)

Example

For n = 4, the possible matrices are [0,0,0,0], [2,0,0,2], [2,0,1,3],[2,0,2,4], [2,1,0,3], [2,2,0,4], [3,0,1,2], [3,0,3,3], [3,1,0,2], [3,1,1,3], [3,1,2,4], [3,2,1,4], [3,3,0,3], [4,0,2,2], [4,1,2,3],
[4,2,0,2], [4,2,1,3] and [4,2,2,4]. There are 18 possibilities.
Here each of the matrices are defined as M = [a,b,c,d], where a = M[1][1], b = M[1][2], c = M[2][1] and d = M[2][2].
So, for n = 4, a(n) = 18.

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+c+d)==(a*d-b*c):
                        s+=1
    return s
for i in range(51):
    print(str(i)+" "+str(t(i)))

Crossrefs

Cf. A210374 (Number of 2 X 2 matrices with all terms in {0,1,...,n} and (sum of terms) = n+2).

Sequence in context: A296843 A200085 A083708 * A191520 A037421 A083423

Adjacent sequences: A280585 A280586 A280587 * A280589 A280590 A280591

Keyword

nonn

Author

Indranil Ghosh, Jan 10 2017

Status

approved