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

0,2

Comments

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

For a guide to related sequences, see A212959.

Links

Table of n, a(n) for n=0..39.

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

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.: f(x)/g(x), where f(x) = (4*x + 3*x^2 + 4*x^3 + x^4) and g(x) = (1+x+x^2)*(1-x)^4.

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 *)

Crossrefs

Cf. A212959, A212973.

Sequence in context: A015653 A106199 A113289 * A033813 A296295 A296268

Adjacent sequences: A212971 A212972 A212973 * A212975 A212976 A212977

Keyword

nonn,easy

Author

Clark Kimberling, Jun 03 2012

Status

approved