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%I #12 Jan 27 2016 06:04:19
%S 1,4,11,18,30,41,58,73,95,114,141,164,196,223,260,291,333,368,415,454,
%T 506,549,606,653,715,766,833,888,960,1019,1096,1159,1241,1308,1395,
%U 1466,1558,1633,1730,1809,1911,1994,2101,2188,2300,2391,2508,2603,2725,2824
%N Number of (w,x,y) with all terms in {0,...,n} and |w-x|+|x-y| = w+x+y.
%C a(n) + A213480(n) = (n+1)^3.
%C For a guide to related sequences, see A212959.
%H Colin Barker, <a href="/A213479/b213479.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 (1,2,-2,-1,1).
%F a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5).
%F G.f.: (1 + 3*x + 5*x^2 + x^3 - x^4)/((1 - x)^3 * (1 + x)^2).
%F From _Colin Barker_, Jan 27 2016: (Start)
%F a(n) = (18*n^2+2*(-1)^n*n+42*n+5*(-1)^n+11)/16.
%F a(n) = (9*n^2+22*n+8)/8 for n even.
%F a(n) = (9*n^2+20*n+3)/8 for n odd. (End)
%t t = Compile[{{n, _Integer}}, Module[{s = 0},
%t (Do[If[w + x + y == Abs[w - x] + Abs[x - y], s = s + 1],
%t {w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];
%t Map[t[#] &, Range[0, 60]] (* A213479 *)
%o (PARI) Vec((1+3*x+5*x^2+x^3-x^4)/((1-x)^3*(1+x)^2) + O(x^100)) \\ _Colin Barker_, Jan 27 2016
%Y Cf. A212959.
%K nonn,easy
%O 0,2
%A _Clark Kimberling_, Jun 13 2012
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