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A196245 Positive integers a for which there is a (-3/4)-Pythagorean triple (a,b,c) satisfying a<=b.

%I A196245 #9 Mar 30 2012 18:57:49
%S A196245 3,3,4,6,6,6,7,8,9,9,9,10,11,12,12,12,12,12,14,14,15,15,16,17,18,18,
%T A196245 18,18,20,20,20,21,21,21,21,22,22,23,24,24,24,24,24,25,26,27,27,27,28,
%U A196245 28,28,28,29,30,30,30,30,30,31,32,32,32,32,33,33,34,34,35,35,36
%N A196245 Positive integers a for which there is a (-3/4)-Pythagorean triple (a,b,c) satisfying a<=b.
%C A196245 See A195770 for definitions of k-Pythagorean triple, primitive k-Pythagorean triple, and lists of related sequences.
%t A196245 z8 = 900; z9 = 250; z7 = 200;
%t A196245 k = -3/4; c[a_, b_] := Sqrt[a^2 + b^2 + k*a*b];
%t A196245 d[a_, b_] := If[IntegerQ[c[a, b]], {a, b, c[a, b]}, 0]
%t A196245 t[a_] := Table[d[a, b], {b, a, z8}]
%t A196245 u[n_] := Delete[t[n], Position[t[n], 0]]
%t A196245 Table[u[n], {n, 1, 15}]
%t A196245 t = Table[u[n], {n, 1, z8}];
%t A196245 Flatten[Position[t, {}]]
%t A196245 u = Flatten[Delete[t, Position[t, {}]]];
%t A196245 x[n_] := u[[3 n - 2]];
%t A196245 Table[x[n], {n, 1, z7}]  (* A196245 *)
%t A196245 y[n_] := u[[3 n - 1]];
%t A196245 Table[y[n], {n, 1, z7}]  (* A196247 *)
%t A196245 z[n_] := u[[3 n]];
%t A196245 Table[z[n], {n, 1, z7}]  (* A196248 *)
%t A196245 x1[n_] := If[GCD[x[n], y[n], z[n]] == 1, x[n], 0]
%t A196245 y1[n_] := If[GCD[x[n], y[n], z[n]] == 1, y[n], 0]
%t A196245 z1[n_] := If[GCD[x[n], y[n], z[n]] == 1, z[n], 0]
%t A196245 f = Table[x1[n], {n, 1, z9}];
%t A196245 x2 = Delete[f, Position[f, 0]]  (* A196249 *)
%t A196245 g = Table[y1[n], {n, 1, z9}];
%t A196245 y2 = Delete[g, Position[g, 0]]  (* A196250 *)
%t A196245 h = Table[z1[n], {n, 1, z9}];
%t A196245 z2 = Delete[h, Position[h, 0]]  (* A196246 *)
%Y A196245 Cf. A195770, A196247, A196248, A196249.
%K A196245 nonn
%O A196245 1,1
%A A196245 _Clark Kimberling_, Sep 30 2011