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A212682 Number of (w,x,y,z) with all terms in {1,...,n} and |x-y|>=|y-z|.

%I A212682 #11 Aug 08 2025 15:12:12
%S A212682 0,1,12,57,168,395,792,1435,2400,3789,5700,8261,11592,15847,21168,
%T A212682 27735,35712,45305,56700,70129,85800,103971,124872,148787,175968,
%U A212682 206725,241332,280125,323400,371519,424800,483631,548352,619377,697068
%N A212682 Number of (w,x,y,z) with all terms in {1,...,n} and |x-y|>=|y-z|.
%C A212682 For a guide to related sequences, see A211795.
%H A212682 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (3,-1,-5,5,1,-3,1).
%F A212682 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 A212682 G.f.: (x + 9*x^2 + 22*x^3 + 14*x^4 + 3*x^5 - x^6)/(1 - 3*x + x^2 + 5*x^3 - 5*x^4 - x^5 + 3*x^6 - x^7).
%t A212682 t = Compile[{{n, _Integer}}, Module[{s = 0},
%t A212682 (Do[If[Abs[x - y] >= Abs[y - z], s = s + 1],
%t A212682 {w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
%t A212682 Map[t[#] &, Range[0, 40]]   (* A212682 *)
%t A212682 LinearRecurrence[{3, -1, -5, 5, 1, -3, 1}, {0, 1, 12, 57, 168, 395, 792}, 40]
%Y A212682 Cf. A211795.
%K A212682 nonn,easy
%O A212682 0,3
%A A212682 _Clark Kimberling_, May 24 2012