A064363 Number of 2 X 2 regular integer matrices with elements from {0,...,n} up to row and column permutation.

0, 2, 14, 51, 133, 289, 547, 954, 1546, 2380, 3508, 5005, 6915, 9347, 12353, 16028, 20468, 25790, 32054, 39427, 47965, 57833, 69155, 82082, 96682, 113192, 131720, 152429, 175467, 201075, 229305, 260492, 294700, 332182, 373138, 417751, 466201

Offset: 0

Author

Vladeta Jovovic, Sep 25 2001

Keywords

• nonn
• nice
• easy

Examples

			There are 2 binary regular matrices up to row and column permutation:
[1 0] [1 1]
[0 1] [1 0].
		

Crossrefs

Cf. A064276, A059306, A062801, A059976, A039623.

Programs

Mathematica

A059306[0] = 1; A059306[n_] := Table[{w, x, y, z} /. {ToRules[ Reduce[0 <= x <= n && 0 <= y <= n && 0 <= z <= n && w*z - x*y == 0, {x, y, z}, Integers]]}, {w, 0, n}] // Flatten[#, 1] & // Length; a[n_] := ((n + 1)*(n^3 + 3*n^2 + 4*n + 1) - A059306[n])/4; Table[Print[an = a[n]]; an, {n, 0, 36}] (* Jean-François Alcover, Nov 26 2013 *)

Formula

a(n) = ((n+1)*(n^3+3*n^2+4*n+1)-A059306(n))/4.