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%I #13 Jan 28 2016 07:52:17
%S 1,6,21,48,93,158,249,368,521,710,941,1216,1541,1918,2353,2848,3409,
%T 4038,4741,5520,6381,7326,8361,9488,10713,12038,13469,15008,16661,
%U 18430,20321,22336,24481,26758,29173,31728,34429,37278,40281,43440,46761,50246,53901
%N Number of (w,x,y) with all terms in {0,...,n} and 2|w-x| >= max(w,x,y)-min(w,x,y).
%C a(n)+A171218(n) = (n+1)^3.
%C For a guide to related sequences, see A212959.
%H Colin Barker, <a href="/A213388/b213388.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2,-2,3,-1).
%F a(n) = 3*a(n-1)-2*a(n-2)-2*a(n-3)+3*a(n-4)-a(n-5).
%F G.f.: ((1 + 3*x + 5*x^2 + x^3)/((1 - x)^4*(1 + x))).
%F From _Colin Barker_, Jan 28 2016: (Start)
%F a(n) = (8*n^3+30*n^2+28*n+3*((-1)^n+3))/12.
%F a(n) = (4*n^3+15*n^2+14*n+6)/6 for n even.
%F a(n) = (4*n^3+15*n^2+14*n+3)/6 for n odd.
%F (End)
%t t = Compile[{{n, _Integer}}, Module[{s = 0},
%t (Do[If[Max[w, x, y] - Min[w, x, y] <= 2 Abs[w - x], s = s + 1], {w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];
%t m = Map[t[#] &, Range[0, 45]] (* A213388 *)
%o (PARI) Vec((1+3*x+5*x^2-x^3)/((1-x)^4*(1+x)) + O(x^100)) \\ _Colin Barker_, Jan 28 2016
%Y Cf. A212959.
%K nonn,easy
%O 0,2
%A _Clark Kimberling_, Jun 11 2012
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