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A212505
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Number of (w,x,y,z) with all terms in {1,...,n} and w<2x and y>=2z.
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2
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0, 0, 3, 14, 48, 114, 243, 444, 768, 1220, 1875, 2730, 3888, 5334, 7203, 9464, 12288, 15624, 19683, 24390, 30000, 36410, 43923, 52404, 62208, 73164, 85683, 99554, 115248, 132510, 151875, 173040, 196608, 222224, 250563, 281214, 314928
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OFFSET
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0,3
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COMMENTS
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For a guide to related sequences, see A211795.
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LINKS
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FORMULA
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a(n) = 2a(n-1)+2a(n-2)-6a(n-3)+6a(n-5)-2a(n-6)-2a(n-7)+a(n-8).
G.f.: x^2*(x^2+2*x+3)*(3*x^2+2*x+1) / ((x+1)^3*(1-x)^5). (End)
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MAPLE
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a:= n-> floor(n^2/4)*ceil(n^2*3/4):
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MATHEMATICA
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t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[w < 2 x && y >= 2 z, s = s + 1],
{w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
Map[t[#] &, Range[0, 40]] (* A212505 *)
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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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STATUS
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approved
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