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A212686 Number of (w,x,y,z) with all terms in {1,...,n} and 2|w-x|=n+|y-z|.

%I A212686 #10 Jun 13 2015 00:54:14
%S A212686 0,0,4,8,24,40,76,112,176,240,340,440,584,728,924,1120,1376,1632,1956,
%T A212686 2280,2680,3080,3564,4048,4624,5200,5876,6552,7336,8120,9020,9920,
%U A212686 10944,11968,13124,14280,15576,16872,18316,19760,21360,22960
%N A212686 Number of (w,x,y,z) with all terms in {1,...,n} and 2|w-x|=n+|y-z|.
%C A212686 a(n)=4*A005993(n-2) for n>=2.
%C A212686 For a guide to related sequences, see A211795.
%H A212686 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2, 1, -4, 1, 2, -1).
%F A212686 a(n)=2*a(n-1)+a(n-2)-4*a(n-3)+a(n-4)+2*a(n-5)-a(n-6).
%F A212686 G.f.: (4*x^2 + 4*x^4)/(1 - 2*x - x^2 + 4*x^3 - x^4 - 2*x^5 + x^6).
%t A212686 t = Compile[{{n, _Integer}}, Module[{s = 0},
%t A212686 (Do[If[2 Abs[w - x] == n + Abs[y - z], s = s + 1],
%t A212686 {w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
%t A212686 Map[t[#] &, Range[0, 40]]   (* A212686 *)
%t A212686 %/4  (* A005993 *)
%t A212686 LinearRecurrence[{2, 1, -4, 1, 2, -1}, {0, 0, 4, 8, 24, 40}, 40]
%Y A212686 Cf. A211795.
%K A212686 nonn,easy
%O A212686 0,3
%A A212686 _Clark Kimberling_, May 25 2012