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

1,2

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

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)

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 *)

Crossrefs

Cf. A210000.

Sequence in context: A217074 A110424 A114079 * A002595 A263956 A229638

Adjacent sequences: A211062 A211063 A211064 * A211066 A211067 A211068

Keyword

nonn

Author

Clark Kimberling, Mar 31 2012

Status

approved