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%I #9 Dec 02 2017 08:48:23
%S 0,0,4,24,84,220,480,924,1624,2664,4140,6160,8844,12324,16744,22260,
%T 29040,37264,47124,58824,72580,88620,107184,128524,152904,180600,
%U 211900,247104,286524,330484,379320,433380,493024,558624,630564,709240,795060,888444
%N Number of (w,x,y,z) with all terms in {1,...,n} and median<mean.
%C Also, the number of (w,x,y,z) with all terms in {1,...,n} and median>mean.
%C For a guide to related sequences, see A211795.
%H Colin Barker, <a href="/A212135/b212135.txt">Table of n, a(n) for n = 0..1001</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F a(n) + A212134(n) = n^4.
%F a(n) = n*(n - 1)*(n^2 - n + 2)/2.
%F a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).
%F G.f.: 4*x*(1 + x + x^2) / (1 - x)^5. - _Colin Barker_, Dec 02 2017
%t t = Compile[{{n, _Integer}}, Module[{s = 0}, (Do[If[
%t Apply[Plus, Rest[Most[Sort[{w, x, y, z}]]]]/2 > (w + x + y + z)/4, s = s + 1], {w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
%t Flatten[Map[{t[#]} &, Range[0, 20]]] (* A212135 *)
%t %/4 (* A002817 *)
%o (PARI) concat(vector(2), Vec(4*x*(1 + x + x^2) / (1 - x)^5 + O(x^40))) \\ _Colin Barker_, Dec 02 2017
%Y Cf. A211795.
%K nonn,easy
%O 0,3
%A _Clark Kimberling_, May 05 2012
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