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A212740
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Number of (w,x,y,z) with all terms in {0,...,n} and max{w,x,y,z}<2*min{w,x,y,z}.
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4
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0, 1, 2, 17, 32, 97, 162, 337, 512, 881, 1250, 1921, 2592, 3697, 4802, 6497, 8192, 10657, 13122, 16561, 20000, 24641, 29282, 35377, 41472, 49297, 57122, 66977, 76832, 89041, 101250, 116161, 131072, 149057, 167042, 188497, 209952
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OFFSET
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0,3
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COMMENTS
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LINKS
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FORMULA
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a(n) = 2*a(n-1)+2*a(n-2)-6*a(n-3)+6*a(n-5)-2*a(n-6)-2*a(n-7)+a(n-8).
G.f.: -x*(1+x^2)*(x^4+10*x^2+1) / ( (1+x)^3*(x-1)^5 ).
a(n) = 3*n^2/8 +1/16 +n^4/8 -(-1)^n/16 -3*(-1)^n*n^2/8. - R. J. Mathar, Jul 01 2013
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MATHEMATICA
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t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[Max[w, x, y, z] < 2 Min[w, x, y, z], s = s + 1],
{w, 0, n}, {x, 0, n}, {y, 0, n}, {z, 0, n}]; s)]];
Map[t[#] &, Range[0, 40]] (* A212740 *)
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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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