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A213490 Number of (w,x,y) with all terms in {0,...,n} and the numbers w,x,y,|w-x|,|x-y| distinct.

%I A213490 #14 Feb 19 2024 10:27:26
%S A213490 0,0,0,0,0,12,38,92,160,286,422,632,870,1194,1542,2010,2502,3126,3788,
%T A213490 4598,5446,6472,7532,8786,10092,11604,13164,14964,16812,18912,21074,
%U A213490 23504,25996,28786,31634,34796,38034,41598,45234,49230,53298
%N A213490 Number of (w,x,y) with all terms in {0,...,n} and the numbers w,x,y,|w-x|,|x-y| distinct.
%C A213490 For a guide to related sequences, see A212959.
%H A213490 <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 A213490 a(n) = a(n-1) + a(n-2) - 2*a(n-5) + a(n-8) + a(n-9) - a(n-10).
%F A213490 G.f.: (12*x^5 + 26*x^6 + 42*x^7 + 30*x^8 + 34*x^9)/(1 - x - x^2 + 2*x^5 - x^8 - x^9 + x^10).
%F A213490 a(n) = (n+1)^3 - A213491(n).
%t A213490 t = Compile[{{n, _Integer}}, Module[{s = 0},
%t A213490  (Do[If[Length[Union[{w, x, y, Abs[w - x],
%t A213490   Abs[x - y]}]] == 5,
%t A213490 s = s + 1], {w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];
%t A213490 m = Map[t[#] &, Range[0, 60]]   (* this sequence *)
%t A213490 LinearRecurrence[{1, 1, 0, 0, -2, 0, 0, 1, 1, -1}, {0, 0, 0, 0, 0, 12, 38, 92, 160, 286}, 60]
%t A213490 m/2 (* integers *)
%Y A213490 Cf. A212959, A213491.
%K A213490 nonn,easy
%O A213490 0,6
%A A213490 _Clark Kimberling_, Jun 13 2012