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A212690 Number of (w,x,y,z) with all terms in {1,...,n} and 2|w-x|<=n+|y-z|.

%I A212690 #9 Aug 01 2015 10:27:18
%S A212690 0,1,16,75,236,567,1172,2157,3672,5861,8920,13031,18436,25355,34076,
%T A212690 44857,58032,73897,92832,115171,141340,171711,206756,246885,292616,
%U A212690 344397,402792,468287,541492,622931,713260,813041,922976,1043665
%N A212690 Number of (w,x,y,z) with all terms in {1,...,n} and  2|w-x|<=n+|y-z|.
%C A212690 a(n)+A212689(n)=n^4.
%C A212690 For a guide to related sequences, see A211795.
%H A212690 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (3, -1, -5, 5, 1, -3, 1).
%F A212690 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 A212690 G.f.: (x + 13*x^2 + 28*x^3 + 32*x^4 + 9*x^5 + x^6)/(1 - 3*x + x^2 + 5*x^3 - 5*x^4 - x^5 + 3*x^6 - x^7).
%t A212690 t = Compile[{{n, _Integer}}, Module[{s = 0},
%t A212690 (Do[If[2 Abs[w - x] <= n + Abs[y - z], s = s + 1],
%t A212690 {w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
%t A212690 Map[t[#] &, Range[0, 40]]   (* A212690 *)
%t A212690 LinearRecurrence[{3, -1, -5, 5, 1, -3, 1}, {0, 1, 16, 75, 236, 567, 1172}, 40]
%Y A212690 Cf. A211795.
%K A212690 nonn,easy
%O A212690 0,3
%A A212690 _Clark Kimberling_, May 25 2012