> lower.pascal(5)
     [,1] [,2] [,3] [,4] [,5]
[1,]    1    0    0    0    0
[2,]    1    1    0    0    0
[3,]    1    2    1    0    0
[4,]    1    3    3    1    0
[5,]    1    4    6    4    1
> lower.pascal.alt(5)
     [,1] [,2] [,3] [,4] [,5]
[1,]    1    0    0    0    0
[2,]    1    1    0    0    0
[3,]    1    2    1    0    0
[4,]    1    3    3    1    0
[5,]    1    4    6    4    1
> upper.pascal(5)
     [,1] [,2] [,3] [,4] [,5]
[1,]    1    1    1    1    1
[2,]    0    1    2    3    4
[3,]    0    0    1    3    6
[4,]    0    0    0    1    4
[5,]    0    0    0    0    1
> symm.pascal(5)
     [,1] [,2] [,3] [,4] [,5]
[1,]    1    1    1    1    1
[2,]    1    2    3    4    5
[3,]    1    3    6   10   15
[4,]    1    4   10   20   35
[5,]    1    5   15   35   70