A067751 - OEIS

%I #8 Sep 21 2013 13:13:15

%S 3,6,7,9,9,12,9,15,12,12,15,19,9,18,18,18,15,18,15,27,18,12,21,30,12,

%T 24,22,21,21,24,21,30,18,18,30,36,9,24,30,30,27,24,15,39,27,18,33,37,

%U 18,30,30,27,21,36,30,48,18,12,39,42,21,30,39,33,30,36,15,45,30,24,45,45,15

%N Number of solutions in nonnegative integers of xy+xz+yz=n.

%C An upper bound on the number of solutions appears to be 9*sqrt(n). - _T. D. Noe_, Jun 14 2006

%H T. D. Noe, <a href="/A067751/b067751.txt">Table of n, a(n) for n = 1..10000</a>

%e a(3)=7 because of (0,1,3),(0,3,1),(1,0,3),(1,3,0),(3,0,1),(3,1,0),(1,1,1).

%t CntFunc[s_List] := Module[{len=Length[Union[s]]}, If[len==3,6,If[len==2,3,1]]]; Table[cnt=0; Do[z=(n-x*y)/(x+y); If[IntegerQ[z], cnt=cnt+CntFunc[{x,y,z}]], {x,0,Sqrt[n/3]}, {y, Max[1,x],Sqrt[x^2+n]-x}]; cnt, {n,100}] - _T. D. Noe_, Jun 14 2006

%Y Cf. A067752, A067753, A067754.

%K easy,nonn

%O 1,1

%A _Colin Mallows_, Jan 31 2002

%E Corrected and extended by _T. D. Noe_, Jun 14 2006