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A212754 Number of (w,x,y,z) with all terms in {0,...,n} and at least one of these conditions holds: wR, y>R, z>R, where R = max{w,x,y,z} - min{w,x,y,z}.

%I A212754 #14 Jun 13 2015 00:54:14
%S A212754 0,8,53,184,472,1008,1905,3296,5336,8200,12085,17208,23808,32144,
%T A212754 42497,55168,70480,88776,110421,135800,165320,199408,238513,283104,
%U A212754 333672,390728,454805,526456,606256,694800,792705,900608,1019168
%N A212754 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 A212754 For a guide to related sequences, see A211795.
%H A212754 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (4,-5,0,5,-4,1).
%F A212754 a(n)=4*a(n-1)-5*a(n-2)+5*a(n-4)-4*a(n-5)+a(n-6).
%F A212754 G.f.: -x*(8+21*x+12*x^2+x^3) / ( (1+x)*(x-1)^5 ).
%t A212754 t = Compile[{{n, _Integer}},
%t A212754 Module[{s = 0}, (Do[
%t A212754 If[(w < # || x > # || y > # || z > #) &[
%t A212754 Max[w, x, y, z] - Min[w, x, y, z]], s++], {w, 0, n},
%t A212754 {x, 0, n}, {y, 0, n}, {z, 0, n}]; s)]];
%t A212754 Map[t[#] &, Range[0, 40]] (* A212754 *)
%t A212754 (* _Peter J. C. Moses_, May 24 2012 *)
%Y A212754 Cf. A211795.
%K A212754 nonn,easy
%O A212754 0,2
%A A212754 _Clark Kimberling_, May 28 2012