A211057 Number of 2 X 2 matrices having all terms in {1,...,n} and determinant in the closed interval [0,n].

1, 10, 36, 91, 179, 330, 516, 802, 1150, 1615, 2119, 2873, 3595, 4558, 5653, 6967, 8245, 10020, 11642, 13846, 16053, 18524, 20944, 24393, 27405, 30924, 34637, 39035, 42961, 48396, 52906, 58687, 64326, 70457, 76722, 84824, 91318, 99045

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

Mathematica

a = 1; b = n; z1 = 40;
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], {n, 1, z1}]