A210375 - OEIS

%I #17 Jul 16 2024 13:14:28

%S 0,1,16,44,80,125,180,246,324,415,520,640,776,929,1100,1290,1500,1731,

%T 1984,2260,2560,2885,3236,3614,4020,4455,4920,5416,5944,6505,7100,

%U 7730,8396,9099,9840,10620,11440,12301,13204,14150,15140,16175,17256,18384,19560

%N Number of 2 X 2 matrices with all terms in {0,1,...,n} and (sum of terms) = n + 3.

%C A210375 is also the number of 2 X 2 matrices with all terms in {0,1,...,n} and (sum of terms) = 3n - 3.

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4, -6, 4, -1).

%F From _Colin Barker_, Dec 07 2017: (Start)

%F G.f.: x*(1 + 12*x - 14*x^2 - 4*x^3 + 6*x^4) / (1 - x)^4.

%F a(n) = (-120 + 74*n + 15*n^2 + n^3) / 6 for n > 1.

%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n > 5.

%F (End)

%t See A210000 for a guide to related sequences.

%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 + 3], {n, 0, z1}]   (* A210375 *)

%t Table[c[n, 3 n - 3], {n, 0, z1}] (* A210375 *)

%Y Cf. A210000.

%K nonn

%O 0,3

%A _Clark Kimberling_, Mar 20 2012