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

%I #6 Dec 04 2016 19:46:29

%S 0,1,4,9,20,29,42,55,80,109,132,153,196,221,254,287,356,389,460,497,

%T 568,617,670,715,808,897,960,1057,1156,1213,1306,1367,1512,1589,1672,

%U 1749,1964,2037,2130,2223,2376,2457,2580,2665,2824,2997,3110

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

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

%e The four (w,x,y,z) counted by a(2): (1,1,1,1), (1,2,1,2), (2,1,2,1), (2,2,2,2).

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

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

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

%t Map[t[#] &, Range[0, 60]] (* A212101 *)

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

%Y Cf. A211795.

%K nonn

%O 0,3

%A _Clark Kimberling_, May 03 2012