%I #13 Jan 09 2024 16:36:11
%S 1,4,13,32,63,108,171,256,365,500,665,864,1099,1372,1687,2048,2457,
%T 2916,3429,4000,4631,5324,6083,6912,7813,8788,9841,10976,12195,13500,
%U 14895,16384,17969,19652,21437,23328,25327,27436,29659,32000
%N Number of (w,x,y,z) with all terms in {0,...,n} and 2w=floor((x+y+z)/2).
%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 (4,-7,8,-7,4,-1).
%F a(n)=4*a(n-1)-7*a(n-2)+8*a(n-3)-7*a(n-4)+4*a(n-5)-a(n-6).
%F G.f.: (1 + 4*x^2 + x^4)/((1 - x)^4 * (1 + x^2)).
%t t = Compile[{{n, _Integer}}, Module[{s = 0},
%t (Do[If[2 w == Floor[(x + y + z)/2], s = s + 1],
%t {w, 0, n}, {x, 0, n}, {y, 0, n}, {z, 0, n}]; s)]];
%t Map[t[#] &, Range[0, 45]] (* A212747 *)
%Y Cf. A211795.
%K nonn,easy
%O 0,2
%A _Clark Kimberling_, May 28 2012