A211065 Number of 2 X 2 matrices having all terms in {1,...,n} and odd determinant.

0, 6, 40, 96, 288, 486, 1056, 1536, 2800, 3750, 6120, 7776, 11760, 14406, 20608, 24576, 33696, 39366, 52200, 60000, 77440, 87846, 110880, 124416, 154128, 171366, 208936, 230496, 277200, 303750, 360960, 393216, 462400, 501126, 583848

Offset: 1

Author

Clark Kimberling, Mar 31 2012

Keywords

• nonn

Comments

A211064(n)+A211065(n)=4^n.

For a guide to related sequences, see A210000.

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A210000.

Programs

Mathematica

a = 1; 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]
u[n_] := Sum[c[n, 2 k], {k, -2*n^2, 2*n^2}]
v[n_] := Sum[c[n, 2 k - 1], {k, -2*n^2, 2*n^2}]
Table[u[n], {n, 1, z1}] (* A211064 *)
Table[v[n], {n, 1, z1}] (* A211065 *)

Formula

From Chai Wah Wu, Nov 27 2016: (Start)

a(n) = (2*n + 1 -(-1)^n)^2*(6*n + 1 -(-1)^n)*(2*n - 1 + (-1)^n)/128.

a(n) = a(n-1) + 4*a(n-2) - 4*a(n-3) - 6*a(n-4) + 6*a(n-5) + 4*a(n-6) - 4*a(n-7) - a(n-8) + a(n-9) for n > 9.

G.f.: -2*x^2*(3*x^5 + 5*x^4 + 28*x^3 + 16*x^2 + 17*x + 3)/((x - 1)^5*(x + 1)^4).

(End)