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

%I A211057 #14 Sep 06 2024 12:40:44
%S A211057 1,10,36,91,179,330,516,802,1150,1615,2119,2873,3595,4558,5653,6967,
%T A211057 8245,10020,11642,13846,16053,18524,20944,24393,27405,30924,34637,
%U A211057 39035,42961,48396,52906,58687,64326,70457,76722,84824,91318,99045
%N A211057 Number of 2 X 2 matrices having all terms in {1,...,n} and determinant in the closed interval [0,n].
%C A211057 For a guide to related sequences, see A210000.
%H A211057 Robert Israel, <a href="/A211057/b211057.txt">Table of n, a(n) for n = 1..1000</a>
%p A211057 g:= proc(n) local T,S,a,b,t,i;
%p A211057   T:= Vector(n^2):
%p A211057   for a from 1 to n do T[a^2]:= 1 od:
%p A211057   for a from 1 to n-1 do for b from a+1 to n do
%p A211057     T[a*b]:= T[a*b]+2
%p A211057   od od;
%p A211057   S:= Vector(n^2);
%p A211057   S[1]:= T[1];
%p A211057   for i from 2 to n^2 do S[i]:= S[i-1]+T[i] od;
%p A211057   t:= T[1]*S[n+1];
%p A211057   for i from 2 to n^2-n do
%p A211057     t:= t + T[i]*(S[i+n]-S[i-1])
%p A211057   od;
%p A211057   t+1
%p A211057 end proc:
%p A211057 g(1):= 1:
%p A211057 map(g, [$1..40]); # _Robert Israel_, Sep 06 2024
%t A211057 a = 1; b = n; z1 = 40;
%t A211057 t[n_] := t[n] = Flatten[Table[w*z - x*y, {w, a, b}, {x, a, b}, {y, a, b}, {z, a, b}]]
%t A211057 c[n_, k_] := c[n, k] = Count[t[n], k]
%t A211057 c1[n_, m_] := c1[n, m] = Sum[c[n, k], {k, 0, m}]
%t A211057 Table[c1[n, n], {n, 1, z1}]
%Y A211057 Cf. A210000.
%K A211057 nonn
%O A211057 1,2
%A A211057 _Clark Kimberling_, Mar 31 2012