A211064 Number of 2 X 2 matrices having all terms in {1,...,n} and even determinant.

1, 10, 41, 160, 337, 810, 1345, 2560, 3761, 6250, 8521, 12960, 16801, 24010, 30017, 40960, 49825, 65610, 78121, 100000, 117041, 146410, 168961, 207360, 236497, 285610, 322505, 384160, 430081, 506250, 562561, 655360, 723521, 835210

Offset: 1

Author

Clark Kimberling, Mar 31 2012

Keywords

• nonn

Comments

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

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

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

a(n) = n^4 - (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.: x*(-x^7 - 9*x^6 - 51*x^5 - 59*x^4 - 83*x^3 - 27*x^2 - 9*x - 1)/((x - 1)^5*(x + 1)^4). (End)