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A212687 Number of (w,x,y,z) with all terms in {1,...,n} and 2|w-x|

%I A212687 #10 Aug 01 2015 10:26:21
%S A212687 0,1,12,67,212,527,1096,2045,3496,5621,8580,12591,17852,24627,33152,
%T A212687 43737,56656,72265,90876,112891,138660,168631,203192,242837,287992,
%U A212687 339197,396916,461735,534156,614811,704240,803121,912032,1031697
%N A212687 Number of (w,x,y,z) with all terms in {1,...,n} and 2|w-x|<n+|y-z|.
%C A212687 a(n)+A212688(n)=n^4.
%C A212687 For a guide to related sequences, see A211795.
%H A212687 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (3, -1, -5, 5, 1, -3, 1).
%F A212687 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 A212687 G.f.: (x + 9*x^2 + 32*x^3 + 28*x^4 + 13*x^5 + x^6)/(1 - 3*x + x^2 + 5*x^3 - 5*x^4 - x^5 + 3*x^6 - x^7).
%t A212687 t = Compile[{{n, _Integer}}, Module[{s = 0},
%t A212687 (Do[If[2 Abs[w - x] < n + Abs[y - z], s = s + 1],
%t A212687 {w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
%t A212687 Map[t[#] &, Range[0, 40]]   (* A212687 *)
%t A212687 LinearRecurrence[{3, -1, -5, 5, 1, -3, 1}, {0, 1, 12, 67, 212, 527, 1096}, 40]
%Y A212687 Cf. A211795.
%K A212687 nonn,easy
%O A212687 0,3
%A A212687 _Clark Kimberling_, May 25 2012