[seqfan] Re: polyotessamino defn in A059573

[Peter Munn]

Hi Richard,

I get 8 if the definition means that you cannot use only 1 domino if there
is a configuration with 2 dominoes, and you fix the 4-omino in position
and count different ways of placing the dominoes. So I get 2 ways for the
block 4-omino; 1 way (0 incomplete, as disallowed) for each of L shaped,
I-shaped and N-shaped; and 3 ways (all incomplete) for the T-shaped.

Best Regards,

Peter

> In A059573 there is a claim that the 5 tetrominoes can be
> filled in T(4,2)=8 ways "as completely as possible" with 1x2
> dominoes. How is this count of 8 obtained? I may get 9
> configurations if I allow some of the tilings to be incomplete,
> using D for a square covered by a domino and o for a free
> square: 1 count for the block 4-omino:
> DD
> DD
> 2 ways (one incomplete) for the L shaped:
> DDD
> D
> DDo
> o
> 2 ways (one incomplete) for the I-shaped:
> oDDo
> DDDD
> 2 ways (one incomplete) for the N-shaped:
> DD
>  DD
> oD
>  Do
> 2 ways (both incomplete) for the T-shaped:
> o
> DD
> o
> D
> Do
> o
> Richard Mathar
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