| | | | | | | | | | | | | | | | | | | | | | | |
= | (1 | + | x | + | x2 | + | x3)3 |
= | (1 | + | x | + | x2 | + | x3) |
× | (1 | + | x | + | x2 | + | x3) |
× | (1 | + | x | + | x2 | + | x3) |
= | 1 | ・ | 1 | ・ | 1 | + | 1 | ・ | 1 | ・ | x | + | 1 | ・ | 1 | ・ | x2 | + | 1 | ・ | 1 | ・ | x3 |
+ | 1 | ・ | x | ・ | 1 | + | 1 | ・ | x | ・ | x | + | 1 | ・ | x | ・ | x2 | + | 1 | ・ | x | ・ | x3 |
+ | 1 | ・ | x2 | ・ | 1 | + | 1 | ・ | x2 | ・ | x | + | 1 | ・ | x2 | ・ | x2 | + | 1 | ・ | x2 | ・ | x3 |
+ | 1 | ・ | x3 | ・ | 1 | + | 1 | ・ | x3 | ・ | x | + | 1 | ・ | x3 | ・ | x2 | + | 1 | ・ | x3 | ・ | x3 |
+ | x | ・ | 1 | ・ | 1 | + | x | ・ | 1 | ・ | x | + | x | ・ | 1 | ・ | x2 | + | x | ・ | 1 | ・ | x3 |
+ | x | ・ | x | ・ | 1 | + | x | ・ | x | ・ | x | + | x | ・ | x | ・ | x2 | + | x | ・ | x | ・ | x3 |
+ | x | ・ | x2 | ・ | 1 | + | x | ・ | x2 | ・ | x | + | x | ・ | x2 | ・ | x2 | + | x | ・ | x2 | ・ | x3 |
+ | x | ・ | x3 | ・ | 1 | + | x | ・ | x3 | ・ | x | + | x | ・ | x3 | ・ | x2 | + | x | ・ | x3 | ・ | x3 |
+ | x2 | ・ | 1 | ・ | 1 | + | x2 | ・ | 1 | ・ | x | + | x2 | ・ | 1 | ・ | x2 | + | x2 | ・ | 1 | ・ | x3 |
+ | x2 | ・ | x | ・ | 1 | + | x2 | ・ | x | ・ | x | + | x2 | ・ | x | ・ | x2 | + | x2 | ・ | x | ・ | x3 |
+ | x2 | ・ | x2 | ・ | 1 | + | x2 | ・ | x2 | ・ | x | + | x2 | ・ | x2 | ・ | x2 | + | x2 | ・ | x2 | ・ | x3 |
+ | x2 | ・ | x3 | ・ | 1 | + | x2 | ・ | x3 | ・ | x | + | x2 | ・ | x3 | ・ | x2 | + | x2 | ・ | x3 | ・ | x3 |
+ | x3 | ・ | 1 | ・ | 1 | + | x3 | ・ | 1 | ・ | x | + | x3 | ・ | 1 | ・ | x2 | + | x3 | ・ | 1 | ・ | x3 |
+ | x3 | ・ | x | ・ | 1 | + | x3 | ・ | x | ・ | x | + | x3 | ・ | x | ・ | x2 | + | x3 | ・ | x | ・ | x3 |
+ | x3 | ・ | x2 | ・ | 1 | + | x3 | ・ | x2 | ・ | x | + | x3 | ・ | x2 | ・ | x2 | + | x3 | ・ | x2 | ・ | x3 |
+ | x3 | ・ | x3 | ・ | 1 | + | x3 | ・ | x3 | ・ | x | + | x3 | ・ | x3 | ・ | x2 | + | x3 | ・ | x3 | ・ | x3 |
| | | | | | | | | | | | | | | | | | | | | | | |
= | 1 | + | x | + | x2 | + | x3 |
+ | x | + | x2 | + | x3 | + | x4 |
+ | x2 | + | x3 | + | x4 | + | x5 |
+ | x3 | + | x4 | + | x5 | + | x6 |
+ | x | + | x2 | + | x3 | + | x4 |
+ | x2 | + | x3 | + | x4 | + | x5 |
+ | x3 | + | x4 | + | x5 | + | x6 |
+ | x4 | + | x5 | + | x6 | + | x7 |
+ | x2 | + | x3 | + | x4 | + | x5 |
+ | x3 | + | x4 | + | x5 | + | x6 |
+ | x4 | + | x5 | + | x6 | + | x7 |
+ | x5 | + | x6 | + | x7 | + | x8 |
+ | x3 | + | x4 | + | x5 | + | x6 |
+ | x4 | + | x5 | + | x6 | + | x7 |
+ | x5 | + | x6 | + | x7 | + | x8 |
+ | x6 | + | x7 | + | x8 | + | x9 |
- (1+x+x2+x3)3
=1+3x+6x2+10x3+12x4+12x5+10x6+6x7+3x8+x9
- (1+x+x2+x3)4
=1+4x+10x2+20x3+31x4+40x5+44x6+40x7+31x8+20x9+10x10+4x11+x12
- (1+x+x2+x3)5
=1+5x+15x2+35x3+65x4+101x5+135x6+155x7
+155x8+135x9+101x10+65x11+35x12+15x13+5x14+x15
- (1+x+x2+x3)6
=1+6x+21x2+56x3+120x4+216x5+336x6+456x7+546x8
+580x9+546x10+456x11+336x12+216x13+120x14+56x15+21x16+6x17+x18
- (1+x+x2+x3)7
=1+7x+28x2+84x3+203x4+413x5+728x6+1128x7+1554x8+1918x9+2128x10
+2128x11+1918x12+1554x13+1128x14+728x15+413x16+203x17+84x18+28x19+7x20+x21