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A210290 Number of 2 X 2 matrices with all elements in {0,1,...,n} and nonnegative determinant.

%I A210290 #11 May 05 2020 17:11:17
%S A210290 1,13,56,160,369,733,1328,2216,3505,5285,7680,10792,14809,19813,26024,
%T A210290 33600,42721,53549,66384,81336,98761,118821,141784,167888,197561,
%U A210290 230917,268352,310176,356753,408285,465376,528088,597049,672533,754944,844744,942425
%N A210290 Number of 2 X 2 matrices with all elements in {0,1,...,n} and nonnegative determinant.
%C A210290 See A210000 for a guide to related sequences.
%H A210290 Andrew Howroyd, <a href="/A210290/b210290.txt">Table of n, a(n) for n = 0..1000</a>
%F A210290 a(n) = ((n+1)^4 + A059306(n))/2. - _Andrew Howroyd_, Apr 28 2020
%t A210290 a = 0; b = n; z1 = 45;
%t A210290 t[n_] := t[n] = Flatten[Table[w*z - x*y, {w, a, b}, {x, a, b}, {y, a, b}, {z, a, b}]]
%t A210290 c[n_, k_] := c[n, k] = Count[t[n], k]
%t A210290 c1[n_, m_] := c1[n, m] = Sum[c[n, k], {k, 0, m}]
%t A210290 Table[c1[n, n^2], {n, 0, z1}]   (* A210290 *)
%Y A210290 Cf. A059306, A210000.
%K A210290 nonn
%O A210290 0,2
%A A210290 _Clark Kimberling_, Mar 19 2012
%E A210290 Terms a(34) and beyond from _Andrew Howroyd_, Apr 28 2020