[seqfan] Re: Tatami

[zbi74583.boat at orange.zero.jp]

> There are two different formulas now in the arena. The earlier one of
> http://list.seqfan.eu/pipermail/seqfan/2016-February/016160.html
> S_3 = 2* sum_{k=0.. (n-3)/4} ((n+3)/2-k)* binomial( (n-3)/2-k,k)
> and the later one in
> http://list.seqfan.eu/pipermail/seqfan/2016-March/016243.html
> with a different numerator in the binomial term:
> S_3 = 2* sum_{k=0.. (n-3)/4} ((n+3)/2-k)* binomial( (n-1)/2-k,k)
>
> The first formula gives the sequence
>
> 2, 10, 18, 38, 72, 136, 250, 454, 814, 1446, 2548...
>
> The second formula gives the sequence
>
> 2, 10, 18, 46, 82, 168, 300, 562, 996, 1790, 3140..
>
>
> S1 := proc(n)
>         add( ((n+1)/2-k)*binomial((n-1)/2-k,k),k=0..(n-1)/4) ;
>         %*2 ;
> end proc:
> S3 := proc(n)
>         # http://list.seqfan.eu/pipermail/seqfan/2016-February/016160.html
>         add( ((n+3)/2-k)*binomial((n-3)/2-k,k),k=0..(n-3)/4) ;
>         # http://list.seqfan.eu/pipermail/seqfan/2016-March/016243.html
>         add( ((n+3)/2-k)*binomial((n-1)/2-k,k),k=0..(n-3)/4) ;
>         %*2 ;
> end proc:
> seq(S1(2*k+1)+S3(2*k+1),k=0..10) ;
>
> Richard
>
> --
> Seqfan Mailing list - http://list.seqfan.eu/
>

    I am sorry that the second formula was typo.
    I think that my friend was sleepy when he was writing it.
    We conjectured that number of tiling n x n room, n is odd, is 10 for all n
exept 1.


    Richard

    Thanks for confirming the terms and the formula.



    Yasutoshi