A211058 Number of 2 X 2 matrices having all terms in {1,...,n} and nonnegative determinant.

1, 11, 48, 144, 337, 691, 1256, 2128, 3385, 5139, 7480, 10584, 14521, 19499, 25664, 33184, 42209, 53027, 65736, 80680, 98009, 117979, 140816, 166936, 196441, 229715, 267056, 308816, 355185, 406755, 463576, 526264, 595081, 670419

Offset: 1

Author

Clark Kimberling, Mar 31 2012

Keywords

• nonn

Comments

For a guide to related sequences, see A210000.

Links

• Robert Israel, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A210000.

Programs

Maple

g:= proc(n) local T,a,b,t,i,r;
  T:= Vector(n^2):
  for a from 1 to n do T[a^2]:= 1 od:
  for a from 1 to n-1 do for b from a+1 to n do
    T[a*b]:= T[a*b]+2
  od od;
  r:= n^2;
  t:= T[1]*r;
  for i from 2 to n^2 do
    r:= r - T[i-1];
    t:= t + T[i]*r;
  od;
  t
end proc:
g(1):= 1:
map(g, [$1..40]); # Robert Israel, Sep 06 2024

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], {n, 1, z1}]   (* A211058 *)