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%I #9 Jun 18 2017 02:26:44
%S 1,6,24,58,118,202,324,478,682,926,1232,1586,2014,2498,3068,3702,4434,
%T 5238,6152,7146,8262,9466,10804,12238,13818,15502,17344,19298,21422,
%U 23666,26092,28646,31394,34278,37368,40602,44054,47658,51492
%N Number of (w,x,y,z) with all terms in {0,...,n} and |w-x|+|x-y+|y-z|=n.
%C For a guide to related sequences, see A211795.
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,-4,1,2,-1).
%F a(n) = 2*a(n-1)+a(n-2)-4*a(n-3)+a(n-4)+2*a(n-5)-a(n-6) for n>=1.
%F G.f.: f(x)/g(x), where f(x)=1 + 4*x + 11*x^2 + 8*x^3 + x^4 - 4*x^5 - x^6 and g(x)=((1-x)^4)*(1+x)^2.
%t t = Compile[{{n, _Integer}}, Module[{s = 0},
%t (Do[If[Abs[w - x] + Abs[x - y] + Abs[y - z] == n, s = s + 1], {w, 0, n}, {x, 0, n}, {y, 0, n}, {z, 0, n}]; s)]];
%t m = Map[t[#] &, Range[0, 40]] (* A212904 *)
%Y Cf. A211795.
%K nonn,easy
%O 0,2
%A _Clark Kimberling_, Jun 01 2012
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