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A212752
Number of (w,x,y,z) with all terms in {0,...,n} and at least one of these conditions holds: w<R, x<R, y<R, z>R, where R=max{w,x,y,z}-min{w,x,y,z}.
2
0, 14, 71, 238, 580, 1224, 2265, 3896, 6236, 9550, 13975, 19854, 27336, 36848, 48545, 62944, 80200, 100926, 125271, 153950, 187100, 225544, 269401, 319608, 376260, 440414, 512135, 592606, 681856, 781200, 890625, 1011584, 1144016
OFFSET
0,2
COMMENTS
For a guide to related sequences, see A211795.
FORMULA
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*(14+43*x+68*x^2+46*x^3+14*x^4+x^5) / ( (1+x)^3*(x-1)^5 )
MATHEMATICA
t = Compile[{{n, _Integer}},
Module[{s = 0}, (Do[If[(w < # || x < # || y < # || z > #) &[Max[w, x, y, z] - Min[w, x, y, z]], s++],
{w, 0, n}, {x, 0, n}, {y, 0, n}, {z, 0, n}]; s)]];
Map[t[#] &, Range[0, 40]] (* A212752 *)
(* Peter J. C. Moses, May 24 2012 *)
CROSSREFS
Cf. A211795.
Sequence in context: A352869 A212572 A186707 * A074086 A205335 A212750
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, May 27 2012
STATUS
approved