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A213493 Number of (w,x,y) with all terms in {0,...,n} and the numbers w,x,y,|w-x|,|x-y|,|y-w| distinct.

%I A213493 #15 Feb 19 2024 10:27:23
%S A213493 0,0,0,0,0,0,12,48,96,204,300,480,684,972,1260,1692,2124,2700,3288,
%T A213493 4044,4812,5784,6744,7932,9144,10584,12024,13752,15480,17496,19524,
%U A213493 21864,24216,26916,29604,32664,35748,39204,42660,46548,50436,54756
%N A213493 Number of (w,x,y) with all terms in {0,...,n} and the numbers w,x,y,|w-x|,|x-y|,|y-w| distinct.
%C A213493 Every term is divisible by 12; see A213494.
%C A213493 For a guide to related sequences, see A212959.
%H A213493 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,0,0,-2,0,0,1,1,-1).
%F A213493 a(n) = a(n-1) + a(n-2) - 2*a(n-5) + a(n-8) + a(n-9) - a(n-10).
%F A213493 G.f.: 12*(x^6 + 3*x^7 + 3*x^8 + 5*x^9)/(1 - x - x^2 + 2*x^5 - x^8 - x^9 + x^10).
%t A213493 t = Compile[{{n, _Integer}}, Module[{s = 0},
%t A213493 (Do[If[Length[Union[{w, x, y, Abs[w - x], Abs[x - y], Abs[y - w]}]] ==
%t A213493 6, s = s + 1], {w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];
%t A213493 m = Map[t[#] &, Range[0, 60]]   (* this sequence *)
%t A213493 m/12  (* A213494 *)
%t A213493 LinearRecurrence[{1, 1, 0, 0, -2, 0, 0, 1, 1, -1}, {0, 0, 0, 0, 0, 0, 12, 48, 96, 204}, 60]
%Y A213493 Cf. A212959, A213494.
%K A213493 nonn,easy
%O A213493 0,7
%A A213493 _Clark Kimberling_, Jun 13 2012