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

0,2

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

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 *)

Crossrefs

Cf. A210000.

Sequence in context: A281768 A225892 A366933 * A200431 A172200 A177291

Adjacent sequences: A211137 A211138 A211139 * A211141 A211142 A211143

Keyword

nonn

Author

Clark Kimberling, Apr 02 2012

Status

approved