%I #19 Dec 04 2016 19:46:29

%S 0,0,7,36,117,292,612,1143,1963,3159,4833,7099,10080,13914,18751,

%T 24750,32085,40942,51516,64017,78667,95697,115353,137893,163584,

%U 192708,225559,262440,303669,349576,400500,456795,518827,586971,661617

%N Number of (w,x,y,z) with all terms in {1,...,n} and w<average{x,y,z}.

%C Also, number of (w,x,y,z) with all terms in {1,...,n} and w>average{x,y,z}.

%C a(n) + A212089(n) = n^4.

%C For a guide to related sequences, see A211795.

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (4, -6, 5, -5, 6, -4, 1).

%F a(n) = 4*a(n-1)-6*a(n-2)+5*a(n-3)-5*a(n-4)+6*a(n-5)-4*a(n-6)+a(n-7).

%F G.f.: x^2*(x^4+5*x^3+15*x^2+8*x+7) / ((x^2+x+1)*(1-x)^5). - _Alois P. Heinz_, May 18 2012

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

%t (Do[If[3 w < x + y + z, s = s + 1],

%t {w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];

%t Map[t[#] &, Range[0, 50]] (* A212088 *)

%t FindLinearRecurrence[%]

%t (* _Peter J. C. Moses_, Apr 13 2012 *)

%t LinearRecurrence[{4, -6, 5, -5, 6, -4, 1},{0, 0, 7, 36, 117, 292, 612},35] (* _Ray Chandler_, Aug 02 2015 *)

%Y Cf. A211795, A212069, A212089.

%K nonn,easy

%O 0,3

%A _Clark Kimberling_, May 01 2012