A212974 Number of (w,x,y) with all terms in {0,...,n} and w>floor((x+y)/3).

0, 4, 15, 37, 75, 132, 212, 320, 459, 633, 847, 1104, 1408, 1764, 2175, 2645, 3179, 3780, 4452, 5200, 6027, 6937, 7935, 9024, 10208, 11492, 12879, 14373, 15979, 17700, 19540, 21504, 23595, 25817, 28175, 30672, 33312, 36100, 39039, 42133

Offset: 0

Author

Clark Kimberling, Jun 03 2012

Keywords

• nonn
• easy

Comments

a(n)+A212973(n) = (n+1)^3.

For a guide to related sequences, see A212959.

Links

• Index entries for linear recurrences with constant coefficients, signature (3,-3,2,-3,3,-1).

Crossrefs

Cf. A212959, A212973.

Programs

Mathematica

t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[w > Floor[(x + y)/3], s = s + 1],
{w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];
m = Map[t[#] &, Range[0, 60]]   (* A212974 *)

Formula

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

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