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A212679 Number of (w,x,y,z) with all terms in {1,...,n} and |x-y|=|y-z|.

%I A212679 #7 Aug 01 2015 10:25:09
%S A212679 0,1,8,33,80,165,288,469,704,1017,1400,1881,2448,3133,3920,4845,5888,
%T A212679 7089,8424,9937,11600,13461,15488,17733,20160,22825,25688,28809,32144,
%U A212679 35757,39600,43741,48128,52833,57800,63105,68688,74629,80864
%N A212679 Number of (w,x,y,z) with all terms in {1,...,n} and |x-y|=|y-z|.
%C A212679 For a guide to related sequences, see A211795.
%H A212679 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2, 1, -4, 1, 2, -1).
%F A212679 a(n)=2*a(n-1)+a(n-2)-4*a(n-3)+a(n-4)+2*a(n-5)-a(n-6).
%F A212679 G.f.: (x + 6*x^2 + 16*x^3 + 10*x^4 + 3*x^5)/(1 - 2*x - x^2 + 4*x^3 - x^4 - 2*x^5 + x^6)
%t A212679 t = Compile[{{n, _Integer}}, Module[{s = 0},
%t A212679 (Do[If[Abs[x - y] == Abs[y - z], s = s + 1],
%t A212679 {w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
%t A212679 Map[t[#] &, Range[0, 50]]   (* A212679 *)
%t A212679 LinearRecurrence[{2, 1, -4, 1, 2, -1}, {0, 1, 8, 33, 80, 165}, 50]
%Y A212679 Cf. A211795.
%K A212679 nonn,easy
%O A212679 0,3
%A A212679 _Clark Kimberling_, May 23 2012