[seqfan] Re: Polyominoes (A000105, A000988, A001168) - offset problem

[Jean-Luc Manguin]

Hello everyone,

Thank you Brendan to "bring some water to my mill", and I am sorry to "shake the tree up to the top", but a request (actually 3) on OEIS with "number of fixed/one-sided/free polyominoes" give results that show this question is not definitely clear.
Moreover, the sequences such as A292357 could be strangely impacted if we admit that there is a "zeromino" ; in that case, we should complete the first diagonal with a "1" at the beginning (if I follow your hypothesis), but what should we put in the corresponding line and row ?? And what could mean "a polyomino with height = 0 and width = n" ??
And moreover again, why should we consider there is ONE zeromino ? Why not zero ?

The usual "rule" is (IMO) to exhibit a publication which justify such a choice ; till now, I have seen nothing.

Thank you for your attention.
Best regards,

JLM 

----- Mail original -----
De: "Brendan McKay" <Brendan.McKay at anu.edu.au>
À: "seqfan" <seqfan at list.seqfan.eu>
Envoyé: Jeudi 25 Juin 2020 11:15:55
Objet: [seqfan] Re: Polyominoes (A000105, A000988, A001168) - offset problem

Hi Neil,

Anyone who sees an error on Wikipedia, and knows how to fix it but 
doesn't, is
responsible for the error.

But in this case there is no error.  Wikipedia follows "reliable 
sources" and in this case
the reliable source is Golumb's book "Polyominoes".  From a brief look 
it seems that
Golumb does not recognise a null polyomino (see Fig 1 and Tables 3 and 
D.1), so
Wikipedia is *required* to either also disallow it or to change to a 
different source.

Incidentally, the first comment on A0000105, which is
"A0000105(n) + A030228(n) = A000988(n)", is not correct for n=0 at the 
moment.

Cheers, Brendan.

On 25/6/20 5:27 pm, Neil Sloane wrote:
> Everything in the Wikipedia is inaccurate.

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