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A212749 Number of (w,x,y,z) with all terms in {0,...,n} and at least one of these conditions holds: w=R, x where R = max{w,x,y,z} - min{w,x,y,z}.

%I A212749 #13 Jun 13 2015 00:54:14
%S A212749 1,14,70,222,537,1116,2056,3512,5605,8550,12486,17694,24325,32732,
%T A212749 43072,55776,71001,89262,110710,135950,165121,198924,237480,281592,
%U A212749 331357,387686,450646,521262,599565,686700,782656,888704,1004785
%N A212749 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 A212749 For a guide to related sequences, see A211795.
%H A212749 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (2,2,-6,0,6,-2,-2,1).
%F A212749 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).
%F A212749 G.f.: ( -1-12*x-40*x^2-60*x^3-37*x^4-12*x^5 ) / ( (1+x)^3*(x-1)^5 ).
%t A212749 t = Compile[{{n, _Integer}},
%t A212749 Module[{s = 0}, (Do[
%t A212749 If[(w == # || x < # || y < # || z < #) &[
%t A212749 Max[w, x, y, z] - Min[w, x, y, z]], s++], {w, 0, n},
%t A212749 {x, 0, n}, {y, 0, n}, {z, 0, n}]; s)]];
%t A212749 Map[t[#] &, Range[0, 40]] (* A212749  *)
%t A212749 (* _Peter J. C. Moses_, May 24 2012 *)
%Y A212749 Cf. A211795.
%K A212749 nonn,easy
%O A212749 0,2
%A A212749 _Clark Kimberling_, May 27 2012