A211140 Number of 2 X 2 matrices having all terms in {-n,...,0,...,n} and determinant n.

1, 20, 92, 176, 364, 408, 880, 704, 1420, 1412, 2088, 1552, 3760, 2104, 3808, 4096, 5388, 3400, 7660, 4208, 9160, 7392, 8464, 5952, 15344, 8428, 11656, 11584, 16608, 9208, 22752, 10464, 21132, 16928, 19192, 17952

Offset: 0

Author

Clark Kimberling, Apr 02 2012

Keywords

• nonn

Comments

For a guide to related sequences, see A210000.

Also the number of 2 X 2 matrices having all terms in {-n,...,0,...,n} and permanent n [because #(a,b,c,d) with a,b,c,d in {-n..n} and a*d-b*c=n equals #(a,b,c,d) with a,b,c,d in {-n..n} and a*d+b*c=n. (Replace d with -d)]. - Alois P. Heinz, Jun 26 2012

Links

• Chai Wah Wu, Table of n, a(n) for n = 0..3000

Crossrefs

Cf. A210000.

Programs

Mathematica

a = -n; b = n; z1 = 35;
t[n_] := t[n] = Flatten[Table[w*z - x*y, {w, a, b}, {x, a, b}, {y, a, b}, {z, a, b}]]
c[n_, k_] := c[n, k] = Count[t[n], k]
Table[c[n, n], {n, 0, z1}]  (* A211140 *)