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A213485 Number of (w,x,y) with all terms in {0,...,n} and |w-x|+|x-y|+|y-w| != w+x+y.

%I A213485 #8 Mar 17 2023 02:07:30
%S A213485 0,4,20,54,109,191,309,469,674,930,1246,1628,2079,2605,3215,3915,4708,
%T A213485 5600,6600,7714,8945,10299,11785,13409,15174,17086,19154,21384,23779,
%U A213485 26345,29091,32023,35144,38460,41980,45710,49653,53815,58205
%N A213485 Number of (w,x,y) with all terms in {0,...,n} and |w-x|+|x-y|+|y-w| != w+x+y.
%C A213485 a(n) + A213484 = (n+1)^3.
%C A213485 For a guide to related sequences, see A212959.
%H A213485 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (4,-7,8,-7,4,-1).
%F A213485 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 A213485 G.f.: (x (4 + 4*x + 2*x^2 + x^3 + x^4))/((1 - x)^4 (1 + x^2)).
%t A213485 t = Compile[{{n, _Integer}}, Module[{s = 0},
%t A213485 (Do[If[w + x + y != Abs[w - x] + Abs[x - y] + Abs[y - w], s = s + 1], {w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];
%t A213485 Map[t[#] &, Range[0, 60]]   (* A213485 *)
%Y A213485 Cf. A212959, A213484.
%K A213485 nonn,easy
%O A213485 0,2
%A A213485 _Clark Kimberling_, Jun 13 2012