[seqfan] Re: 3D version of A000938: 3-in-line inside the nXnXn cube

[Ron Hardin]

Looking at the number of sets of 4 collinear points in a 2..9 dimensional side-4 grid

$ awk '{print FILENAME,$4}' stat??4.txt
stat204.txt 10
stat304.txt 76
stat404.txt 520
stat504.txt 3376
stat604.txt 21280
stat704.txt 131776
stat804.txt 807040
stat904.txt 4907776

you get A016149 and A081199

[For 3 points and a 2..9 dimensional side-3 grid

$ awk '{print FILENAME,$3}' stat??3.txt
stat203.txt 8
stat303.txt 49
stat403.txt 272
stat503.txt 1441
stat603.txt 7448
stat703.txt 37969
stat803.txt 192032
stat903.txt 966721

you get A005059]

for 5 points and a 2..9 dimensional side-5 grid

$ awk '{print FILENAME,$5}' stat??5.txt
stat205.txt 12
stat305.txt 109
stat405.txt 888
stat505.txt 6841
stat605.txt 51012
stat705.txt 372709
stat805.txt 2687088
stat905.txt 19200241

you get  A016161 and A081200

for 6 points and a 2..8 dimensional side-6 grid (dim 9 not yet computed)

$ awk '{print FILENAME,$6}' stat??6.txt
stat206.txt 14
stat306.txt 148
stat406.txt 1400
stat506.txt 12496
stat606.txt 107744
stat706.txt 908608
stat806.txt 7548800

you get A016170 and A081201

from which pattern I guess you can guess a formula.



 rhhardin at mindspring.com
rhhardin at att.net (either)