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A212688 Number of (w,x,y,z) with all terms in {1,...,n} and 2|w-x|>=n+|y-z|.

%I A212688 #9 Aug 01 2015 10:26:39
%S A212688 0,0,4,14,44,98,200,356,600,940,1420,2050,2884,3934,5264,6888,8880,
%T A212688 11256,14100,17430,21340,25850,31064,37004,43784,51428,60060,69706,
%U A212688 80500,92470,105760,120400,136544,154224,173604,194718,217740
%N A212688 Number of (w,x,y,z) with all terms in {1,...,n} and 2|w-x|>=n+|y-z|.
%C A212688 a(n)+A212687(n)=n^4.
%C A212688 For a guide to related sequences, see A211795.
%H A212688 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (3, -1, -5, 5, 1, -3, 1).
%F A212688 a(n)=3*a(n-1)-a(n-2)-5*a(n-3)+5*a(n-4)+a(n-5)-3*a(n-6)+a(n-7).
%F A212688 G.f.: (4*x^2 + 2*x^3 + 6*x^4)/(1 - 3*x + x^2 + 5*x^3 - 5*x^4 - x^5 + 3*x^6 - x^7).
%t A212688 t = Compile[{{n, _Integer}}, Module[{s = 0},
%t A212688 (Do[If[2 Abs[w - x] >= n + Abs[y - z], s = s + 1],
%t A212688 {w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
%t A212688 Map[t[#] &, Range[0, 40]]   (* A212688 *)
%t A212688 %/2  (* integers *)
%t A212688 LinearRecurrence[{3, -1, -5, 5, 1, -3, 1}, {0, 0, 4, 14, 44, 98, 200}, 40]
%Y A212688 Cf. A211795.
%K A212688 nonn,easy
%O A212688 0,3
%A A212688 _Clark Kimberling_, May 25 2012