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

0, 0, 10, 40, 85, 140, 206, 284, 375, 480, 600, 736, 889, 1060, 1250, 1460, 1691, 1944, 2220, 2520, 2845, 3196, 3574, 3980, 4415, 4880, 5376, 5904, 6465, 7060, 7690, 8356, 9059, 9800, 10580, 11400, 12261, 13164, 14110, 15100, 16135, 17216

Offset: 0

Author

Clark Kimberling, Mar 20 2012

Keywords

• nonn

Comments

A210376 is also the number of 2 X 2 matrices with all terms in {0,1,...,n} and (sum of terms) = 3n - 4.

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 + 4], {n, 0, z1}]    (* A210376 *)
Table[c[n, 3 n - 4], {n, 0, z1}]  (* A210376 *)

Formula

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

G.f.: x^2*(10 - 15*x^2 + 6*x^4) / (1 - x)^4.

a(n) = (-270 + 107*n + 18*n^2 + n^3) / 6 for n>2.

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

(End)