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A212750 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 where R = max{w,x,y,z} - min{w,x,y,z}.

%I A212750 #15 May 07 2022 10:38:35
%S A212750 1,14,72,216,529,1070,1984,3336,5345,8070,11816,16624,22897,30646,
%T A212750 40384,52080,66369,83166,103240,126440,153681,184734,220672,261176,
%U A212750 307489,359190,417704,482496,555185,635110,724096,821344,928897
%N A212750 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 A212750 For a guide to related sequences, see A211795.
%H A212750 <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 A212750 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 A212750 G.f.:( -1-12*x-42*x^2-50*x^3-37*x^4-6*x^5 ) / ( (1+x)^3*(x-1)^5 ).
%t A212750 t = Compile[{{n, _Integer}},
%t A212750 Module[{s = 0}, (Do[
%t A212750 If[(w == # || x == # || y < # || z < #) &[
%t A212750 Max[w, x, y, z] - Min[w, x, y, z]], s++],
%t A212750 {w, 0, n}, {x, 0, n},{y, 0, n}, {z, 0, n}]; s)]];
%t A212750 Map[t[#] &, Range[0, 40]] (* A212750  *)
%t A212750 (* _Peter J. C. Moses_, May 24 2012 *)
%t A212750 LinearRecurrence[{2,2,-6,0,6,-2,-2,1},{1,14,72,216,529,1070,1984,3336},40] (* _Harvey P. Dale_, May 07 2022 *)
%Y A212750 Cf. A211795.
%K A212750 nonn,easy
%O A212750 0,2
%A A212750 _Clark Kimberling_, May 27 2012