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%I #11 Dec 07 2017 08:37:02
%S 0,0,10,40,85,140,206,284,375,480,600,736,889,1060,1250,1460,1691,
%T 1944,2220,2520,2845,3196,3574,3980,4415,4880,5376,5904,6465,7060,
%U 7690,8356,9059,9800,10580,11400,12261,13164,14110,15100,16135,17216
%N Number of 2 X 2 matrices with all terms in {0,1,...,n} and (sum of terms) = n + 4.
%C A210376 is also the number of 2 X 2 matrices with all terms in {0,1,...,n} and (sum of terms) = 3n - 4.
%C See A210000 for a guide to related sequences.
%F Conjectures from _Colin Barker_, Dec 07 2017: (Start)
%F G.f.: x^2*(10 - 15*x^2 + 6*x^4) / (1 - x)^4.
%F a(n) = (-270 + 107*n + 18*n^2 + n^3) / 6 for n>2.
%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4.
%F (End)
%t a = 0; b = n; z1 = 45;
%t t[n_] := t[n] = Flatten[Table[w + x + y + z, {w, a, b}, {x, a, b}, {y, a, b}, {z, a, b}]]
%t c[n_, k_] := c[n, k] = Count[t[n], k]
%t Table[c[n, n + 4], {n, 0, z1}] (* A210376 *)
%t Table[c[n, 3 n - 4], {n, 0, z1}] (* A210376 *)
%Y Cf. A210000.
%K nonn
%O 0,3
%A _Clark Kimberling_, Mar 20 2012
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