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A210375
Number of 2 X 2 matrices with all terms in {0,1,...,n} and (sum of terms) = n + 3.
2
0, 1, 16, 44, 80, 125, 180, 246, 324, 415, 520, 640, 776, 929, 1100, 1290, 1500, 1731, 1984, 2260, 2560, 2885, 3236, 3614, 4020, 4455, 4920, 5416, 5944, 6505, 7100, 7730, 8396, 9099, 9840, 10620, 11440, 12301, 13204, 14150, 15140, 16175, 17256, 18384, 19560
OFFSET
0,3
COMMENTS
A210375 is also the number of 2 X 2 matrices with all terms in {0,1,...,n} and (sum of terms) = 3n - 3.
FORMULA
From Colin Barker, Dec 07 2017: (Start)
G.f.: x*(1 + 12*x - 14*x^2 - 4*x^3 + 6*x^4) / (1 - x)^4.
a(n) = (-120 + 74*n + 15*n^2 + n^3) / 6 for n > 1.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n > 5.
(End)
MATHEMATICA
See A210000 for a guide to related sequences.
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 + 3], {n, 0, z1}] (* A210375 *)
Table[c[n, 3 n - 3], {n, 0, z1}] (* A210375 *)
CROSSREFS
Cf. A210000.
Sequence in context: A204039 A235413 A238255 * A173560 A293858 A258547
KEYWORD
nonn
AUTHOR
Clark Kimberling, Mar 20 2012
STATUS
approved