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A210376 Number of 2 X 2 matrices with all terms in {0,1,...,n} and (sum of terms) = n + 4.

%I A210376 #13 Jul 16 2024 13:16:36
%S A210376 0,0,10,40,85,140,206,284,375,480,600,736,889,1060,1250,1460,1691,
%T A210376 1944,2220,2520,2845,3196,3574,3980,4415,4880,5376,5904,6465,7060,
%U A210376 7690,8356,9059,9800,10580,11400,12261,13164,14110,15100,16135,17216
%N A210376 Number of 2 X 2 matrices with all terms in {0,1,...,n} and (sum of terms) = n + 4.
%C A210376 A210376 is also the number of 2 X 2 matrices with all terms in {0,1,...,n} and (sum of terms) = 3n - 4.
%C A210376 See A210000 for a guide to related sequences.
%H A210376 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4, -6, 4, -1).
%F A210376 Conjectures from _Colin Barker_, Dec 07 2017: (Start)
%F A210376 G.f.: x^2*(10 - 15*x^2 + 6*x^4) / (1 - x)^4.
%F A210376 a(n) = (-270 + 107*n + 18*n^2 + n^3) / 6 for n>2.
%F A210376 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4.
%F A210376 (End)
%t A210376 a = 0; b = n; z1 = 45;
%t A210376 t[n_] := t[n] = Flatten[Table[w + x + y + z, {w, a, b}, {x, a, b}, {y, a, b}, {z, a, b}]]
%t A210376 c[n_, k_] := c[n, k] = Count[t[n], k]
%t A210376 Table[c[n, n + 4], {n, 0, z1}]    (* A210376 *)
%t A210376 Table[c[n, 3 n - 4], {n, 0, z1}]  (* A210376 *)
%Y A210376 Cf. A210000.
%K A210376 nonn
%O A210376 0,3
%A A210376 _Clark Kimberling_, Mar 20 2012