A210374 Number of 2 X 2 matrices with all terms in {0,1,...,n} and (sum of terms) = n+2.

0, 4, 19, 40, 68, 104, 149, 204, 270, 348, 439, 544, 664, 800, 953, 1124, 1314, 1524, 1755, 2008, 2284, 2584, 2909, 3260, 3638, 4044, 4479, 4944, 5440, 5968, 6529, 7124, 7754, 8420, 9123, 9864, 10644, 11464, 12325, 13228, 14174, 15164

Offset: 0

Author

Clark Kimberling, Mar 20 2012

Keywords

• nonn

Comments

A210374 is also the number of 2 X 2 matrices with all terms in {0,1,...,n} and (sum of terms) = 3n-2.

See A210000 for a guide to related sequences.

Links

• Index entries for linear recurrences with constant coefficients, signature (4, -6, 4, -1).

Crossrefs

Cf. A210000.

Programs

Mathematica

a = 0; b = n; z1 = 45;
t[n_] := t[n] = Flatten[Table[w + x + y + z, {w, a, b}, {x, a, b}, {y, a, b}, {z, a, b}]]
c[n_, k_] := c[n, k] = Count[t[n], k]
Table[c[n, n + 2], {n, 0, z1}]    (* A210374 *)
Table[c[n, 3 n - 2], {n, 0, z1}]  (* A210374 *)

Formula

Conjectures from Colin Barker, Dec 07 2017: (Start)

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

a(n) = (-36 + 47*n + 12*n^2 + n^3) / 6 for n>0.

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

(End)