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A213491 Number of (w,x,y) with all terms in {0,...,n} and the numbers w,x,y,|w-x|,|x-y| not distinct.

%I A213491 #18 Feb 19 2024 13:39:57
%S A213491 1,8,27,64,125,204,305,420,569,714,909,1096,1327,1550,1833,2086,2411,
%T A213491 2706,3071,3402,3815,4176,4635,5038,5533,5972,6519,6988,7577,8088,
%U A213491 8717,9264,9941,10518,11241,11860,12619,13274,14085,14770,15623
%N A213491 Number of (w,x,y) with all terms in {0,...,n} and the numbers w,x,y,|w-x|,|x-y| not distinct.
%C A213491 For a guide to related sequences, see A212959.
%H A213491 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,1,1,-1,-1,-1,0,1).
%F A213491 a(n) = a(n-2) + a(n-3) + a(n-4) - a(n-5) - a(n-6) - a(n-7) + a(n-9).
%F A213491 G.f.: (1 + 8*x + 26*x^2 + 55*x^3 + 89*x^4 + 106*x^5 + 98*x^6 + 63*x^7 + 34*x^8)/(1 - x^2 - x^3 - x^4 + x^5 + x^6 + x^7 - x^9).
%F A213491 a(n) = (n+1)^3 - A213490(n).
%t A213491 t = Compile[{{n, _Integer}}, Module[{s = 0}, (Do[If[Length[Union[{w, x, y, Abs[w - x], Abs[x - y]}]] < 5, s = s + 1], {w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];
%t A213491 m = Map[t[#] &,  Range[0, 60]]
%t A213491 (* or *)
%t A213491 LinearRecurrence[{0, 1, 1, 1, -1, -1, -1, 0, 1}, {1, 8, 27, 64, 125, 204, 305, 420, 569}, 60]
%Y A213491 Cf. A212959, A213490.
%K A213491 nonn,easy
%O A213491 0,2
%A A213491 _Clark Kimberling_, Jun 13 2012