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A212972
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Number of triples (w,x,y) with all terms in {0,...,n} and w >= floor((x+y)/3).
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4
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1, 8, 24, 53, 100, 168, 261, 384, 540, 733, 968, 1248, 1577, 1960, 2400, 2901, 3468, 4104, 4813, 5600, 6468, 7421, 8464, 9600, 10833, 12168, 13608, 15157, 16820, 18600, 20501, 22528, 24684, 26973, 29400, 31968, 34681, 37544, 40560, 43733
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OFFSET
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0,2
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COMMENTS
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For a guide to related sequences, see A212959.
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LINKS
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FORMULA
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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.: (1 + 5x + 3*x^2 + 3*x^3)/((1 + x + x^2)*(1-x)^4).
a(n) = (2*n^3 + 8*n^2 + 10*n + 4 - (((n+1) mod 3) mod 2))/3. (End)
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MATHEMATICA
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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]] (* A212972 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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