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A211140 Number of 2 X 2 matrices having all terms in {-n,...,0,...,n} and determinant n. 2
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 (list; graph; refs; listen; history; text; internal format)
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: A225882 A281768 A225892 * A200431 A172200 A177291

Adjacent sequences:  A211137 A211138 A211139 * A211141 A211142 A211143

KEYWORD

nonn

AUTHOR

Clark Kimberling, Apr 02 2012

STATUS

approved

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Last modified August 2 15:15 EDT 2021. Contains 346428 sequences. (Running on oeis4.)