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A212575 Number of (w,x,y,z) with all terms in {1,...,n} and 2|w-x|=|x-y|+|y-z|.

%I A212575 #10 Aug 01 2015 10:20:57
%S A212575 0,1,4,17,42,85,142,235,346,495,680,911,1172,1505,1872,2305,2798,3365,
%T A212575 3978,4699,5470,6335,7284,8335,9448,10705,12028,13473,15026,16709,
%U A212575 18470,20411,22434,24607,26912,29375,31932,34705,37576,40625,43830
%N A212575 Number of (w,x,y,z) with all terms in {1,...,n} and  2|w-x|=|x-y|+|y-z|.
%C A212575 For a guide to related sequences, see A211795.
%H A212575 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (0, 2, 2, -1, -4, -1, 2, 2, 0, -1).
%F A212575 a(n) = 2*a(n-2)+2*a(n-3)-a(n-4)-4*a(n-5)-a(n-6)+2*a(n-7)+2*a(n-8)-a(n-10).
%F A212575 G.f.: (x + 4*x^2 + 15*x^3 + 32*x^4 + 44*x^5 + 32*x^6 + 15*x^7 + 4*x^8 + x^9)/(1 - 2*x^2 - 2*x^3 + x^4 + 4*x^5 + x^6 - 2*x^7 - 2*x^8 + x^10)
%t A212575 t = Compile[{{n, _Integer}}, Module[{s = 0},
%t A212575 (Do[If[2 Abs[w - x] == Abs[x - y] + Abs[y - z],
%t A212575   s = s + 1],
%t A212575 {w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
%t A212575 Map[t[#] &, Range[0, 40]]   (* A212575 *)
%t A212575 LinearRecurrence[{0, 2, 2, -1, -4, -1, 2, 2, 0, -1}, {0, 1, 4, 17, 42, 85, 142, 235, 346, 495}, 40]
%Y A212575 Cf. A211795.
%K A212575 nonn,easy
%O A212575 0,3
%A A212575 _Clark Kimberling_, May 22 2012