[seqfan] Re: Tatami

Richard J. Mathar mathar at mpia-hd.mpg.de
Sat Apr 30 23:31:55 CEST 2016


In response to http://list.seqfan.eu/pipermail/seqfan/2016-April/016347.html :

>     Let us compute S_1(n) the case n=17
> 
>     n=1  Mod 4  so  k is even
>     0<=k<=[(17-1)/6] , [m] means Floor(m)
>     So
>     k=0 or 2
>     S_1(n)=2*(5*4!/(0!*4!)+4*3!/(2!*1!)=34
> 
>     But your result is 45/8

I don't see that. My result for n=8 was 45/8, as quoted in http://list.seqfan.eu/pipermail/seqfan/2016-April/016342.html. 
My results for n=0 to n=20 are
0, 2, 0, 0, 0, 4, 0, 4, 45/8, 6, 77/8, 12, 117/8, 14, 165/8, 24, 221/8, 34, 285/8, 48, 14739/256,
so I get S_1(17)=34.


The sequence of the number of tatami tilings of the 5x(2n+1) floor with 1 monomer is column m=1 of A272474:
3, 18 ,10, 8, 18, 24, 32, 52, 68, 100, 142, 196,...

Richard Mathar


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