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

1,2

Comments

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

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) = 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)

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: A102784 A294604 A061003 * A048879 A221805 A089211

Adjacent sequences: A211061 A211062 A211063 * A211065 A211066 A211067

Keyword

nonn

Author

Clark Kimberling, Mar 31 2012

Status

approved