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A212758 Number of (w,x,y,z) with all terms in {0,...,n} and w=[R/2], where R=max{w,x,y,z}-min{w,x,y,z} and [ ]=floor.

%I A212758 #10 Jun 13 2015 00:54:14
%S A212758 1,8,20,57,118,172,299,468,594,865,1196,1424,1893,2440,2800,3521,4338,
%T A212758 4860,5887,7028,7742,9129,10648,11584,13385,15336,16524,18793,21230,
%U A212758 22700,25491,28468,30250,33617,37188,39312,43309,47528,50024
%N A212758 Number of (w,x,y,z) with all terms in {0,...,n} and w=[R/2], where R=max{w,x,y,z}-min{w,x,y,z} and [ ]=floor.
%C A212758 For a guide to related sequences, see A211795.
%H A212758 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,3,-3,0,-3,3,0,1,-1).
%F A212758 a(n)=a(n-1)+3*a(n-3)-3*a(n-4)-3*a(n-6)+3*a(n-7)+a(n-9)-a(n-10).
%F A212758 G.f.:  ( 1+7*x+12*x^2+34*x^3+40*x^4+18*x^5+19*x^6+7*x^7 ) / ( (1+x+x^2)^3*(1-x)^4 ).
%t A212758 t = Compile[{{n, _Integer}}, Module[{s = 0},
%t A212758 (Do[If[w == Floor[(Max[w, x, y, z] - Min[w, x, y, z])/2], s = s + 1],
%t A212758 {w, 0, n}, {x, 0, n}, {y, 0, n}, {z, 0, n}]; s)]];
%t A212758 Map[t[#] &, Range[0, 45]]   (* A212758 *)
%t A212758 LinearRecurrence[{1, 0, 3, -3, 0, -3, 3, 0, 1, -1}, {1, 8, 20, 57, 118, 172, 299, 468, 594, 865}, 45]
%Y A212758 Cf. A211795.
%K A212758 nonn
%O A212758 0,2
%A A212758 _Clark Kimberling_, May 28 2012