- #1
sludger13
- 83
- 0
Hi,
(hope it doesn't seem so weird),
I'm looking for a general expanded form of
(x+y+z)^{k}, k\in N
k=1:
x+y+z
k=2:
x^{2}+y^{2}+z^{2}+2xy+2xz+2yz
k=3:
x^{3}+y^{3}+z^{3}+3xy^{2}+3xz^{2}+3yz^{2}+3x^{2}y+3x^{2}z+3y^{2}z+6xyz
k=4:
x^{4}+y^{4}+z^{4}+4xy^{3}+4x^{3}y+4xz^{3}+4x^{3}z+4yz^{3}
+4y^{3}z+6x^{2}y^{2}+6y^{2}z^{2}+6x^{2}z^{2}+12x^{2}yz+12xy^{2}z+12xyz^{2}
The elements are obviously determined by combinations of their powers, which sum is always k.
I just cannot find the algorithm for element's constants.
(hope it doesn't seem so weird),
I'm looking for a general expanded form of
(x+y+z)^{k}, k\in N
k=1:
x+y+z
k=2:
x^{2}+y^{2}+z^{2}+2xy+2xz+2yz
k=3:
x^{3}+y^{3}+z^{3}+3xy^{2}+3xz^{2}+3yz^{2}+3x^{2}y+3x^{2}z+3y^{2}z+6xyz
k=4:
x^{4}+y^{4}+z^{4}+4xy^{3}+4x^{3}y+4xz^{3}+4x^{3}z+4yz^{3}
+4y^{3}z+6x^{2}y^{2}+6y^{2}z^{2}+6x^{2}z^{2}+12x^{2}yz+12xy^{2}z+12xyz^{2}
The elements are obviously determined by combinations of their powers, which sum is always k.
I just cannot find the algorithm for element's constants.
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