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A212974
Number of (w,x,y) with all terms in {0,...,n} and w>floor((x+y)/3).
4
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.
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
Sequence in context: A015653 A106199 A113289 * A033813 A296295 A296268
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jun 03 2012
STATUS
approved