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A212905 Number of (w,x,y,z) with all terms in {0,...,n} and |w-x|+|x-y+|y-z|=2n.

%I A212905 #8 Jun 18 2017 02:26:44
%S A212905 1,6,16,26,42,58,82,106,140,174,220,266,326,386,462,538,632,726,840,
%T A212905 954,1090,1226,1386,1546,1732,1918,2132,2346,2590,2834,3110,3386,3696,
%U A212905 4006,4352,4698,5082,5466,5890,6314,6780,7246,7756,8266,8822
%N A212905 Number of (w,x,y,z) with all terms in {0,...,n} and |w-x|+|x-y+|y-z|=2n.
%C A212905 For a guide to related sequences, see A211795.
%H A212905 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,-4,1,2,-1).
%F A212905 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 A212905 G.f.: f(x)/g(x), where f(x)=1 + 4*x + 3*x^2 - 8*x^3 - 3*x^4 + 4*x^5 + x^6 and g(x)=((1-x)^4)*(1+x)^2.
%t A212905 t = Compile[{{n, _Integer}}, Module[{s = 0},
%t A212905 (Do[If[Abs[w - x] + Abs[x - y] + Abs[y - z] == 2 n, s = s + 1], {w, 0, n}, {x, 0, n}, {y, 0, n}, {z, 0, n}]; s)]];
%t A212905 m = Map[t[#] &, Range[0, 40]]   (* A212905 *)
%Y A212905 Cf. A211795.
%K A212905 nonn,easy
%O A212905 0,2
%A A212905 _Clark Kimberling_, Jun 01 2012