%I #12 Jun 18 2017 02:26:44

%S 1,5,17,38,75,127,203,300,429,585,781,1010,1287,1603,1975,2392,2873,

%T 3405,4009,4670,5411,6215,7107,8068,9125,10257,11493,12810,14239,

%U 15755,17391,19120,20977,22933,25025,27222,29563,32015,34619,37340

%N Number of (w,x,y) with all terms in {0,...,n} and w>=range{w,x,y}.

%C a(n)+A212967(n) = (n+1)^3.

%C For a guide to related sequences, see A212959.

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,-4,1,2,-1).

%F a(n) = (n+1)*(14*n*(n+2)+3*(-1)^n+21)/24.

%F a(n) = 2*a(n-1)+a(n-2)-4*a(n-3)+a(n-4)+2*a(n-5)-a(n-6).

%F G.f.: f(x)/g(x), where f(x) = 1 + 3*x + 6*x^2 + 3*x^3 + x^4 and g(x) = ((1-x)^4)(1+x)^2.

%t t = Compile[{{n, _Integer}}, Module[{s = 0},

%t (Do[If[w >= (Max[w, x, y] - Min[w, x, y]), s = s + 1],

%t {w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];

%t Map[t[#] &, Range[0, 60]] (* A212968 *)

%Y Cf. A212959.

%K nonn,easy

%O 0,2

%A _Clark Kimberling_, Jun 02 2012