A067751 Number of solutions in nonnegative integers of x*y+x*z+y*z = n.
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, 24, 22, 21, 21, 24, 21, 30, 18, 18, 30, 36, 9, 24, 30, 30, 27, 24, 15, 39, 27, 18, 33, 37, 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
Offset: 1
Examples
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).
Links
- T. D. Noe, Table of n, a(n) for n = 1..10000
Programs
-
Mathematica
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 *)
Extensions
Corrected and extended by T. D. Noe, Jun 14 2006
Comments