A210377 Number of 2 X 2 matrices with all terms in {0,1,...,n} and (sum of terms) = n + 5.

0, 0, 4, 31, 80, 146, 224, 315, 420, 540, 676, 829, 1000, 1190, 1400, 1631, 1884, 2160, 2460, 2785, 3136, 3514, 3920, 4355, 4820, 5316, 5844, 6405, 7000, 7630, 8296, 8999, 9740, 10520, 11340, 12201, 13104, 14050, 15040, 16075, 17156, 18284

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 - 5.

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 + 5], {n, 0, z1}]    (* A210377 *)
Table[c[n, 3 n - 5], {n, 0, z1}]  (* A210377 *)

Formula

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

G.f.: x^2*(4 + 15*x - 20*x^2 - 4*x^3 + 6*x^5) / (1 - x)^4.

a(n) = (-504 + 146*n + 21*n^2 + n^3) / 6 for n>3.

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

(End)