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Number of (w,x,y,z) with all terms in {1,...,n} and w*x+y*z<=n^2.
2

%I #5 Dec 04 2016 19:46:30

%S 0,0,9,56,196,499,1074,2014,3497,5658,8705,12811,18278,25239,34099,

%T 45086,58543,74748,94210,117123,144094,175386,211549,252962,300400,

%U 353941,414476,482417,558525,643076,737167,840779,955262,1080987

%N Number of (w,x,y,z) with all terms in {1,...,n} and w*x+y*z<=n^2.

%C A212150(n)+A212136(n)=n^4. For a guide to related sequences, see A211795.

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

%t (Do[If[w*x + y*z <= n^2, s = s + 1],

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

%t Map[t[#] &, Range[0, 40]] (* A212150 *)

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

%Y Cf. A211795.

%K nonn

%O 0,3

%A _Clark Kimberling_, May 07 2012