[seqfan] Re: Number of ways of tiling a n X n X n cube with cubes

[Rob Pratt]

I confirm your values up through n = 5.  Equivalently, this is the number of packings with cubes of side length >= 2.

-----Original Message-----
From: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of Richard J. Mathar
Sent: Saturday, November 25, 2017 12:06 PM
To: seqfan at seqfan.eu
Subject: [seqfan] Number of ways of tiling a n X n X n cube with cubes

EXTERNAL

Is the sequence of the number of ways of tiling the n X n X n cube non-overlapping with cubes in the OEIS? My conjecture is that this starts at offset n=1  with 1, 2, 10, 2098, 4006722,...; it would be nice to have an independent confirmation.

Example: The a(3)=10 ways for the 3 X 3 X 3 cube
1 way to fill it with 27 unit cubes
1 way to fill it with a 3 X 3 X 3 cube
8 ways to place 2 X 2 X 2 cube plus 19 interstitial unit cubes.

This should be the diagonal of A228267.

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