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

%I A211058 #10 Sep 06 2024 14:16:00
%S A211058 1,11,48,144,337,691,1256,2128,3385,5139,7480,10584,14521,19499,25664,
%T A211058 33184,42209,53027,65736,80680,98009,117979,140816,166936,196441,
%U A211058 229715,267056,308816,355185,406755,463576,526264,595081,670419
%N A211058 Number of 2 X 2 matrices having all terms in {1,...,n} and nonnegative determinant.
%C A211058 For a guide to related sequences, see A210000.
%H A211058 Robert Israel, <a href="/A211058/b211058.txt">Table of n, a(n) for n = 1..1000</a>
%p A211058 g:= proc(n) local T,a,b,t,i,r;
%p A211058   T:= Vector(n^2):
%p A211058   for a from 1 to n do T[a^2]:= 1 od:
%p A211058   for a from 1 to n-1 do for b from a+1 to n do
%p A211058     T[a*b]:= T[a*b]+2
%p A211058   od od;
%p A211058   r:= n^2;
%p A211058   t:= T[1]*r;
%p A211058   for i from 2 to n^2 do
%p A211058     r:= r - T[i-1];
%p A211058     t:= t + T[i]*r;
%p A211058   od;
%p A211058   t
%p A211058 end proc:
%p A211058 g(1):= 1:
%p A211058 map(g, [$1..40]); # _Robert Israel_, Sep 06 2024
%t A211058 a = 1; b = n; z1 = 35;
%t A211058 t[n_] := t[n] = Flatten[Table[w*z - x*y, {w, a, b}, {x, a, b}, {y, a, b}, {z, a, b}]]
%t A211058 c[n_, k_] := c[n, k] = Count[t[n], k]
%t A211058 c1[n_, m_] := c1[n, m] = Sum[c[n, k], {k, 0, m}]
%t A211058 Table[c1[n, n^2], {n, 1, z1}]   (* A211058 *)
%Y A211058 Cf. A210000.
%K A211058 nonn
%O A211058 1,2
%A A211058 _Clark Kimberling_, Mar 31 2012