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A212577 Number of (w,x,y,z) with all terms in {1,...,n} and |w-x|=2|x-y|-|y-z|.

%I A212577 #16 May 03 2019 09:44:32
%S A212577 0,1,4,17,46,89,154,251,374,531,736,979,1268,1621,2024,2485,3026,3629,
%T A212577 4302,5071,5914,6839,7876,8999,10216,11561,13004,14553,16246,18049,
%U A212577 19970,22051,24254,26587,29096,31739,34524,37501,40624,43901
%N A212577 Number of (w,x,y,z) with all terms in {1,...,n} and |w-x|=2|x-y|-|y-z|.
%C A212577 For a guide to related sequences, see A211795.
%H A212577 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (2, -1, 2, -4, 2, -1, 2, -1).
%F A212577 a(n) = 2*a(n-1)-a(n-2)+2*a(n-3)-4*a(n-4)+2*a(n-5)-a(n-6)+2*a(n-7)-a(n-8).
%F A212577 G.f.: (x + 2*x^2 + 10*x^3 + 14*x^4 + 10*x^5 + 2*x^6 + x^7)/(1 - 2*x + x^2 - 2*x^3 + 4*x^4 - 2*x^5 + x^6 - 2*x^7 + x^8). [corrected by _Georg Fischer_, May 03 2019]
%t A212577 t = Compile[{{n, _Integer}}, Module[{s = 0},
%t A212577 (Do[If[Abs[w - x] == 2 Abs[x - y] - Abs[y - z],
%t A212577   s = s + 1],
%t A212577 {w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
%t A212577 Map[t[#] &, Range[0, 40]]   (* A212577 *)
%t A212577 LinearRecurrence[{2, -1, 2, -4, 2, -1, 2, -1}, {0, 1, 4, 17, 46, 89, 154, 251}, 45]
%Y A212577 Cf. A211795.
%K A212577 nonn,easy
%O A212577 0,3
%A A212577 _Clark Kimberling_, May 22 2012