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A212756 Number of (w,x,y,z) with all terms in {0,...,n} and 2w-x=max{w,x,y,z}-min{w,x,y,z}.

%I A212756 #9 Aug 01 2015 10:28:51
%S A212756 1,4,17,32,71,104,187,247,380,484,685,823,1122,1311,1690,1963,2452,
%T A212756 2767,3416,3806,4557,5079,5982,6546,7679,8342,9591,10442,11885,12770,
%U A212756 14521,15529,17402,18662,20771,22049,24552,25977,28600,30349
%N A212756 Number of (w,x,y,z) with all terms in {0,...,n} and 2w-x=max{w,x,y,z}-min{w,x,y,z}.
%C A212756 For a guide to related sequences, see A211795.
%H A212756 <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (-2, 0, 5, 7, 0, -9, -9, 0, 7, 5, 0, -2, -1).
%F A212756 a(n)=-2*a(n-1)+5*a(n-3)+7*a(n-4)-9*a(n-6)-9*a(n-7)+7*a(n-9)+5*a(n-10)-2*a(n-12)-a(n-13).
%F A212756 G.f.: ( 1+6*x+25*x^2+61*x^3+108*x^4+133*x^5+125*x^6+87*x^7+46*x^8+15*x^9+3*x^10 ) / ( (1+x)^3*(1+x+x^2)^3*(x-1)^4 ).
%t A212756 t = Compile[{{n, _Integer}}, Module[{s = 0},
%t A212756 (Do[If[2 w == x + Max[w, x, y, z] - Min[w, x, y, z],
%t A212756   s = s + 1],
%t A212756 {w, 0, n}, {x, 0, n}, {y, 0, n}, {z, 0, n}]; s)]];
%t A212756 Map[t[#] &, Range[0, 45]]   (* A212756 *)
%t A212756 LinearRecurrence[{-2, 0, 5, 7, 0, -9, -9, 0, 7, 5, 0, -2, -1}, {1, 4, 17, 32, 71, 104, 187, 247, 380, 484, 685, 823, 1122}, 45]
%Y A212756 Cf. A211795.
%K A212756 nonn,easy
%O A212756 0,2
%A A212756 _Clark Kimberling_, May 28 2012