A212752 - OEIS

%I #11 Dec 04 2016 19:46:30

%S 0,14,71,238,580,1224,2265,3896,6236,9550,13975,19854,27336,36848,

%T 48545,62944,80200,100926,125271,153950,187100,225544,269401,319608,

%U 376260,440414,512135,592606,681856,781200,890625,1011584,1144016

%N Number of (w,x,y,z) with all terms in {0,...,n} and at least one of these conditions holds: w<R, x<R, y<R, z>R, where R=max{w,x,y,z}-min{w,x,y,z}.

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

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (2,2,-6,0,6,-2,-2,1).

%F a(n)=2*a(n-1)+2*a(n-2)-6*a(n-3)+6*a(n-5)-2*a(n-6)-2*a(n-7)+a(n-8).

%F G.f.: -x*(14+43*x+68*x^2+46*x^3+14*x^4+x^5) / ( (1+x)^3*(x-1)^5 )

%t t = Compile[{{n, _Integer}},

%t Module[{s = 0}, (Do[If[(w < # || x < # || y < # || z > #) &[Max[w, x, y, z] - Min[w, x, y, z]], s++],

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

%t Map[t[#] &, Range[0, 40]] (* A212752 *)

%t (* _Peter J. C. Moses_, May 24 2012 *)

%Y Cf. A211795.

%K nonn,easy

%O 0,2

%A _Clark Kimberling_, May 27 2012