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A212753 Number of (w,x,y,z) with all terms in {0,...,n} and at least one of these conditions holds: wR, z>R, where R = max{w,x,y,z} - min{w,x,y,z}.

%I A212753 #13 Jun 13 2015 00:54:14
%S A212753 0,12,69,228,568,1192,2225,3816,6136,9380,13765,19532,26944,36288,
%T A212753 47873,62032,79120,99516,123621,151860,184680,222552,265969,315448,
%U A212753 371528,434772,505765,585116,673456,771440,879745,999072,1130144
%N A212753 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}.
%C A212753 For a guide to related sequences, see A211795.
%H A212753 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (4,-5,0,5,-4,1).
%F A212753 a(n)=4*a(n-1)-5*a(n-2)+5*a(n-4)-4*a(n-5)+a(n-6).
%F A212753 G.f.: -x*(12+21*x+12*x^2+x^3) / ( (1+x)*(x-1)^5 ).
%t A212753 t = Compile[{{n, _Integer}},
%t A212753 Module[{s = 0}, (Do[
%t A212753 If[(w < # || x < # || y > # || z > #) &[
%t A212753 Max[w, x, y, z] - Min[w, x, y, z]], s++], {w, 0, n},
%t A212753 {x, 0, n}, {y, 0, n}, {z, 0, n}]; s)]];
%t A212753 Map[t[#] &, Range[0, 40]]  (* A212753 *)
%t A212753 (* _Peter J. C. Moses_, May 24 2012 *)
%Y A212753 Cf. A211795.
%K A212753 nonn,easy
%O A212753 0,2
%A A212753 _Clark Kimberling_, May 28 2012