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A212692 Number of (w,x,y,z) with all terms in {1,...,n} and w<|x-y|+|y-z|.

%I A212692 #10 Aug 01 2015 10:27:55
%S A212692 0,0,6,22,54,106,184,292,436,620,850,1130,1466,1862,2324,2856,3464,
%T A212692 4152,4926,5790,6750,7810,8976,10252,11644,13156,14794,16562,18466,
%U A212692 20510,22700,25040,27536,30192,33014,36006,39174,42522,46056,49780
%N A212692 Number of (w,x,y,z) with all terms in {1,...,n} and w<|x-y|+|y-z|.
%C A212692 For a guide to related sequences, see A211795.
%H A212692 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (3, -2, -2, 3, -1).
%F A212692 a(n) = 3*a(n-1)-2*a(n-2)-2*a(n-3)+3*a(n-4)-a(n-5).
%F A212692 G.f.: (6*x^2 + 4*x^3)/(1 - 3*x + 2* x^2 + 2*x^3 - 3*x^4 + x^5).
%t A212692 t = Compile[{{n, _Integer}}, Module[{s = 0},
%t A212692 (Do[If[w == Abs[x - y] + Abs[y - z], s = s + 1],
%t A212692 {w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
%t A212692 Map[t[#] &, Range[0, 40]]   (* A212692 *)
%t A212692 %/2  (* integers *)
%t A212692 LinearRecurrence[{3, -2, -2, 3, -1}, {0, 0, 6, 22, 54}, 40]
%Y A212692 Cf. A211795.
%K A212692 nonn,easy
%O A212692 0,3
%A A212692 _Clark Kimberling_, May 23 2012