A209981 Number of singular 2 X 2 matrices having all elements in {-n,...,n}.

1, 33, 129, 289, 545, 833, 1313, 1729, 2369, 3041, 3905, 4577, 5857, 6657, 7905, 9345, 10881, 11937, 13953, 15137, 17441, 19521, 21537, 22977, 26177, 28257, 30657, 33249, 36577, 38401, 42721, 44673, 48257, 51617, 54785, 58529, 63905

Offset

0,2

Comments

See A210000 for a guide to related sequences.

Links

Chai Wah Wu, Table of n, a(n) for n = 0..10000

Formula

a(n) = 8*A134506(n) + (4*n + 1)^2. - Andrew Howroyd, May 04 2020

Example

Among the 33 matrices counted by a(1) are these (in compact notation):
(-1,-1,-1,-1), (0,0,0,0), (1,-1,-1,1), (1,1,1,1).

Mathematica

a = -n; b = n; z1 = 40;
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, 0], {n, 0, z1}]  (* A209981 *)
Table[c[n, 1], {n, 0, z1}]  (* A209982 *)
%/4                         (* A206258 *)
2 %                         (* A209983 *)
Table[c[n, 2], {n, 0, z1}]  (* A209984 *)
%/4                         (* A209985 *)
Table[c[n, 3], {n, 0, z1}]  (* A209986 *)
%/8                         (* A209987 *)
Table[c[n, 4], {n, 0, z1}]  (* A209988 *)
%/4                         (* A209989 *)
Table[c[n, 5], {n, 0, z1}]  (* A209990 *)
%/8                         (* A209997 *)

Crossrefs

Cf. A210000.

Sequence in context: A010020 A007419 A158575 * A036546 A043502 A044365

Adjacent sequences: A209978 A209979 A209980 * A209982 A209983 A209984

Keyword

nonn

Author

Clark Kimberling, Mar 17 2012

Status

approved