A210374 - OEIS

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

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OFFSET

0,2

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

Table of n, a(n) for n=0..41.

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

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)

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 *)

CROSSREFS

Cf. A210000.

Sequence in context: A003338 A344189 A031291 * A352116 A283394 A134538

Adjacent sequences: A210371 A210372 A210373 * A210375 A210376 A210377

KEYWORD

nonn

AUTHOR

Clark Kimberling, Mar 20 2012

STATUS

approved