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Number of (w,x,y,z) with all terms in {1,...,n} and w*x<=y*z+1.
3

%I #8 Dec 04 2016 19:46:29

%S 0,1,13,56,158,365,725,1312,2198,3477,5245,7624,10742,14725,19725,

%T 25920,33470,42557,53397,66176,81150,98525,118533,141456,167606,

%U 197189,230509,267920,309726,356205,407805,464744,527494,596389,671789

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

%C a(n)+A212054(n)=n^4. See A211795 for a guide to related sequences.

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

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

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

%t Map[t[#] &, Range[0, 50]] (* A212053 *)

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

%Y Cf. A211795.

%K nonn

%O 0,3

%A _Clark Kimberling_, Apr 29 2012