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

[Ron Hardin]

I get

3 49
4 376
5 1858
6 5696
7 16427
8 36992
9 78204
10 150672
11 277005
12 463624
13 776494
14 1212208
15 1845911
16 2749568
17 4023608
18 5654976
19 7915497
20 10730616
21 14487706
22 19290352
23 25343011

which was checked only by agreement with yours, ie is probably right, i guess.

more terms to follow.

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



----- Original Message ----
> From: Richard Mathar <mathar at strw.leidenuniv.nl>
> To: seqfan at seqfan.eu
> Sent: Fri, May 21, 2010 8:46:47 AM
> Subject: [seqfan]  3D version of A000938: 3-in-line inside the nXnXn cube
> 
> 
What is the 3D variant of A000938?
This should count the number of 
> collinear point-triples in the n X n X n cube (i.d.,
in the simple cubic 
> lattice). By scanning the binomial(n^3,3) 
triples of distinct points in the 
> cube (which is C(n^3,3) = 2925, 41664, 317750,...for n>=3),
I guess this 
> starts (offset n=3): 49,376,1858,5696 (? to be confirmed)