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%I #10 May 07 2019 18:32:50
%S 1,4,13,26,45,66,95,126,163,204,251,300,357,416,481,550,625,702,787,
%T 874,967,1064,1167,1272,1385,1500,1621,1746,1877,2010,2151,2294,2443,
%U 2596,2755,2916,3085,3256,3433,3614,3801,3990,4187,4386,4591
%N Number of (w,x,y,z) with all terms in {0,...,n} and equal consecutive gap sizes.
%C The gap sizes are |w-x|, |x-y|, |y-z|. For a guide to related sequences, see A211795.
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,0,-1,-1,1).
%F a(n) = a(n-1)+a(n-2)-a(n-4)-a(n-5)+a(n-6).
%F G.f.: f(x)/g(x), where f(x) = 1 + 3*x + 8*x^2 + 9*x^3 + 7*x^4 and g(x) = (1 + 2*x + 2*x^2 + x^3)(1 - x)^3.
%e a(1)=4 counts these (w,x,y,z): (0,0,0,0), (1,1,1,1), (0,1,0,1), (1,0,1,0).
%t t = Compile[{{n, _Integer}}, Module[{s = 0},
%t (Do[If[Abs[w - x] == Abs[x - y] == Abs[y - z], s = s + 1], {w, 0, n}, {x, 0, n}, {y, 0, n}, {z, 0, n}]; s)]];
%t m = Map[t[#] &, Range[0, 40]] (* A212901 *)
%Y Cf. A211795, A212900.
%K nonn,easy
%O 0,2
%A _Clark Kimberling_, May 31 2012
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