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A212568 Number of (w,x,y,z) with all terms in {1,...,n} and w<|x-y|+|y-z|.

%I A212568 #16 May 03 2019 08:44:20
%S A212568 0,0,2,24,98,272,608,1184,2092,3440,5350,7960,11422,15904,21588,28672,
%T A212568 37368,47904,60522,75480,93050,113520,137192,164384,195428,230672,
%U A212568 270478,315224,365302,421120,483100,551680,627312,710464,801618
%N A212568 Number of (w,x,y,z) with all terms in {1,...,n} and  w<|x-y|+|y-z|.
%C A212568 a(n) + A212675(n) = n^4.
%C A212568 For a guide to related sequences, see A211795.
%H A212568 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (4, -5, 0, 5, -4, 1).
%F A212568 a(n) = 4*a(n-1)-5*a(n-2)+5*a(n-4)-4*a(n-5)+a(n-6).
%F A212568 G.f.: (2*x^2+16*x^3+12*x^4)/(1-4*x+5*x^2-5*x^4+4*x^5-x^6). [corrected by _Georg Fischer_, May 03 2019]
%t A212568 t = Compile[{{n, _Integer}}, Module[{s = 0},
%t A212568 (Do[If[w < Abs[x - y] + Abs[y - z], s = s + 1],
%t A212568 {w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
%t A212568 Map[t[#] &, Range[0, 40]]   (* A212568 *)
%t A212568 %/2 (* integers *)
%t A212568 LinearRecurrence[{4, -5, 0, 5, -4, 1}, {0, 0, 2, 24, 98, 272}, 20]
%Y A212568 Cf. A211795.
%K A212568 nonn,easy
%O A212568 0,3
%A A212568 _Clark Kimberling_, May 23 2012