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A212579 Number of (w,x,y,z) with all terms in {1,...,n} and min{|w-x|,|w-y|}=min{|x-y|,|x-z|}.

%I A212579 #18 Apr 25 2024 10:41:14
%S A212579 0,1,8,31,80,171,308,509,780,1137,1584,2143,2812,3615,4552,5645,6892,
%T A212579 8321,9924,11731,13736,15967,18416,21117,24056,27269,30744,34515,
%U A212579 38568,42943,47620,52641,57988,63701,69760,76211,83028,90259,97880
%N A212579 Number of (w,x,y,z) with all terms in {1,...,n} and min{|w-x|,|w-y|}=min{|x-y|,|x-z|}.
%C A212579 For a guide to related sequences, see A211795.
%H A212579 Bertrand Teguia Tabuguia, <a href="https://arxiv.org/abs/2401.00256">Hypergeometric-Type Sequences</a>, arXiv:2401.00256 [cs.SC], 2023.
%H A212579 Bertrand Teguia Tabuguia, <a href="https://arxiv.org/abs/2404.10143">Computing with Hypergeometric-Type Terms</a>, arXiv:2404.10143 [cs.SC], 2024.
%H A212579 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-1,-2,-1,2,1,-1).
%F A212579 a(n) = a(n-1)+2*a(n-2)-a(n-3)-2*a(n-4)-a(n-5)+2*a(n-6)+a(n-7)-a(n-8).
%F A212579 G.f.: (x + 7*x^2 + 21*x^3 + 34*x^4 + 39*x^5 + 25*x^6 + 7*x^7)/(1 - x - 2* x^2 + x^3 + 2*x^4 + x^5 - 2*x^6 - x^7 + x^8).
%t A212579 t = Compile[{{n, _Integer}}, Module[{s = 0},
%t A212579 (Do[If[Min[Abs[w - x], Abs[w - y]] == Min[Abs[x - y], Abs[x - z]],
%t A212579 s = s + 1],
%t A212579 {w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
%t A212579 Map[t[#] &, Range[0, 40]]   (* A212579 *)
%t A212579 LinearRecurrence[{1, 2, -1, -2, -1, 2, 1, -1}, {0, 1, 8, 31, 80, 171, 308, 509}, 50]
%Y A212579 Cf. A211795.
%K A212579 nonn,easy
%O A212579 0,3
%A A212579 _Clark Kimberling_, May 22 2012