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%I #15 Feb 20 2024 11:18:33
%S 0,0,0,2,6,19,29,52,81,116,159,223,282,366,462,568,688,841,987,1170,
%T 1371,1586,1821,2101,2372,2692,3036,3398,3786,4231,4665,5160,5685,
%U 6232,6811,7459,8094,8802,9546,10316,11124,12013,12887,13846,14847
%N Number of (w,x,y) with all terms in {0,...,n} and w < R < 2*w, where R = range{w,x,y} = max(w,x,y)-min(w,x,y).
%C For a guide to related sequences, see A212959.
%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,2,-1,-4,-1,2,2,0,-1).
%F a(n) = 2*a(n-2)+2*a(n-3)-a(n-4)-4*a(n-5)-a(n-6)+2*a(n-7)+2*a(n-8)-a(n-10).
%F G.f.: (2*x^3 + 6*x^4 + 15*x^5 + 13*x^6 + 4*x^7 - x^8 - x^9 )/(1 - 2*x^2 - 2*x^3 + x^4 + 4*x^5 + x^6 - 2*x^7 - 2*x^8 + x^10).
%t t = Compile[{{n, _Integer}}, Module[{s = 0}, (Do[If[w < Max[w, x, y] - Min[w, x, y] < 2 w, s = s + 1], {w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];
%t m = Map[t[#] &, Range[0, 60]] (* A213400 *)
%Y Cf. A212959.
%K nonn,easy
%O 0,4
%A _Clark Kimberling_, Jun 12 2012
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