A211056 Number of 2 X 2 nonsingular matrices having all terms in {1,...,n}.

0, 10, 66, 224, 576, 1210, 2290, 3936, 6352, 9722, 14322, 20304, 28080, 37834, 49922, 64704, 82624, 103898, 129170, 158640, 192944, 232554, 278050, 329680, 388368, 454522, 528770, 611680, 704192, 806490, 919890, 1044624, 1181680

Offset: 1

Author

Clark Kimberling, Mar 31 2012

Keywords

• nonn

Comments

A211056(n) + A134506(n) = n^4.

For a guide to related sequences, see A210000.

Crossrefs

Cf. A134506, A210000, A211059.

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]
c1[n_, m_] := c1[n, m] = Sum[c[n, k], {k, 0, m}]
Table[c1[n, n^2] - c[n, 0], {n, 1, z1}]   (* A211059 *)
2*%     (* A211056 *)