A067751 Number of solutions in nonnegative integers of xy+xz+yz=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

1,1

Comments

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

Links

T. D. Noe, Table of n, a(n) for n = 1..10000

Example

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).

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

Crossrefs

Cf. A067752, A067753, A067754.

Sequence in context: A181919 A021735 A121550 * A283762 A088045 A267983

Adjacent sequences: A067748 A067749 A067750 * A067752 A067753 A067754

Keyword

easy,nonn

Author

Colin Mallows, Jan 31 2002

Extensions

Corrected and extended by T. D. Noe, Jun 14 2006

Status

approved