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A213489 Number of (w,x,y) with all terms in {0,...,n} and |w-x| + |x-y| + |y-w| >= w + x + y.

%I A213489 #13 May 10 2019 18:38:55
%S A213489 1,7,19,37,64,103,154,217,295,391,505,637,790,967,1168,1393,1645,1927,
%T A213489 2239,2581,2956,3367,3814,4297,4819,5383,5989,6637,7330,8071,8860,
%U A213489 9697,10585,11527,12523,13573,14680,15847,17074,18361,19711,21127
%N A213489 Number of (w,x,y) with all terms in {0,...,n} and |w-x| + |x-y| + |y-w| >= w + x + y.
%C A213489 For a guide to related sequences, see A212959.
%H A213489 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (4,-7,8,-7,4,-1).
%F A213489 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 A213489 G.f.: (1 + 3*x - 2*x^2 + 2* x^3 - x^5)/((1 - x)^4 (1 + x^2)). [corrected by _Georg Fischer_, May 10 2019]
%F A213489 a(n) + A213488(n) = (n+1)^3.
%t A213489 t = Compile[{{n, _Integer}}, Module[{s = 0},
%t A213489 (Do[If[w + x + y <= Abs[w - x] + Abs[x - y] + Abs[y - w],
%t A213489 s = s + 1], {w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];
%t A213489 m = Map[t[#] &, Range[0, 60]]   (* A213489 *)
%Y A213489 Cf. A212959, A213488.
%K A213489 nonn,easy
%O A213489 0,2
%A A213489 _Clark Kimberling_, Jun 13 2012